ワダ タツアキ和田 達明教授Tatsuaki WADA
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(研究者からのメッセージ)
(研究経歴),・ 超高真空中におけるGaAs光電面に関する研究,・ 数値繰り込み法の一種であるDMRG(密度行列繰り込み法)に関する研究,・ 非加法的エントロピに基づく統計力学の拡張に関する研究,・ 一般化エントロピに関する数理構造,・ 一般化エントロピに基づく統計力学と情報幾何学との関連,・ 量子反射に関する研究,・ 量子ウォーク,・ 変形指数分布族に関する情報幾何構造
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論文
- 〔主要な業績〕A Hamiltonian approach to the gradient-flow equations in information geometry
Tatsuaki Wada; Antonio M. Scarfone, Abstract: We have studied the gradient-flow equations in information geometry from a point-particle perspective. Based on the motion of a null (or light-like) particle in a curved space, we have rederived the Hamiltonians which describe the gradient-flows in information geometry. Graphical abstract: (Figure presented.)
European Physical Journal B, 2024年07月 - 〔主要な業績〕Multi-Additivity in Kaniadakis Entropy
Antonio M. Scarfone; Tatsuaki Wada, ラスト(シニア)オーサー, It is known that Kaniadakis entropy, a generalization of the Shannon–Boltzmann–Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number (Formula presented.) that makes Kaniadakis entropy multi-additive, i.e., (Formula presented.), under the composition of two statistically independent and identically distributed distributions (Formula presented.), with reduced distributions (Formula presented.) and (Formula presented.) belonging to the same class.
Entropy, 2024年01月, ［査読有り］ - 〔主要な業績〕Mechanics of geodesics in information geometry and black hole thermodynamics
Sumanto Chanda; Tatsuaki Wada, ラスト(シニア)オーサー, In this paper, we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers–Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner–Nordström black holes., World Scientific Pub Co Pte Ltd
International Journal of Geometric Methods in Modern Physics, 2023年12月29日, ［査読有り］ - 〔主要な業績〕Huygens' equations and the gradient-flow equations in information geometry
Tatsuaki Wada; Antonio M. Scarfone; Hiroshi Matsuzoe, 筆頭著者, In this paper, we revisit the relation between the gradient-flow equations and Hamilton's equations in information geometry. By regarding the gradient-flow equations as Huygens' equations in geometric optics, we have related the gradient flows to the geodesic flows induced by the geodesic Hamiltonian in an appropriate Riemannian geometry. The original evolution parameter t in the gradient-flow equations is related to the arc-length parameter in the associated Riemannian manifold by Jacobi-Maupertuis transformation. As a by-product, the relation between the gradient-flow equation and replicator equations is found.
International Journal of Geometric Methods in Modern Physics, 2023年12月15日, ［査読有り］ - 〔主要な業績〕On the Kaniadakis Distributions Applied in Statistical Physics and Natural Sciences
T. Wada and A.M. Scarfone, 筆頭著者, Constitutive relations are fundamental and essential to characterize physical systems. By utilizing the κ,-deformed functions, some constitutive relations are generalized. We here show some applications of the Kaniadakis distributions, based on the inverse hyperbolic sine function, to some topics belonging to the realm of statistical physics and natural science., MDPI
Entropy, 2023年02月04日, ［査読有り］, ［招待有り］ - 〔主要な業績〕WEYL GEOMETRIC APPROACH TO THE GRADIENT-FLOW EQUATIONS IN INFORMATION GEOMETRY
Tatsuaki Wada, 筆頭著者, The gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations associated with the gradient-flow equations are regarded as the general pre-geodesic equations in the Weyl integrable geometry.
Journal of Geometry and Symmetry in Physics, 2023年, ［査読有り］ - 〔主要な業績〕Weyl geometry and the gradient-flow equations in information geometry.
Tatsuaki Wada
CoRR, 2022年 - 〔主要な業績〕An eikonal equation approach to thermodynamics and the gradient flows in information geometry
TatsuakiWada; Antonio M. Scarfone; Hiroshi Matsuzoe, 筆頭著者, We can incorporate a “time” evolution into thermodynamics as a Hamilton–Jacobi dynamics. A set of the equations of state in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton–Jacobi equation. We relate the Hamilton–Jacobi dynamics of a simple thermodynamic system to the gradient flows in information geometry., Elsevier
Physica A, 2021年05月, ［査読有り］ - Huygens' equations and the gradient-flow equations in information geometry.
Tatsuaki Wada; Antonio Maria Scarfone; Hiroshi Matsuzoe, In this paper, we revisit the relation between the gradient-flow equations and Hamilton's equations in information geometry. By regarding the gradient-flow equations as Huygens' equations in geometric optics, we have related the gradient flows to the geodesic flows induced by the geodesic Hamiltonian in an appropriate Riemannian geometry. The original evolution parameter t in the gradient-flow equations is related to the arc-length parameter in the associated Riemannian manifold by Jacobi-Maupertuis transformation. As a by-product, the relation between the gradient-flow equation and replicator equations is found.
CoRR, 2021年 - A study of Rényi entropy based on the information geometry formalism
Antonio M Scarfone; Hiroshi Matsuzoe; Tatsuaki Wada, ラスト(シニア)オーサー, In the framework of information geometry, we explore the structure of statistical manifold related to the Rényi entropy. Starting from a new family of generalized exponential distributions given by the equilibrium distribution of a canonical system described by the Rényi entropy, we introduce on a dually-flat geometry endowed by a Hessian structure derived from a generalization of the Fisher metric and a flat affine connection. This geometrical structure admits a Legendre transform that links the thermodynamic potentials of the underlying statistical mechanics to the dual potentials of the corresponding information geometry. A canonical divergence function à la Bregman is naturally derived in this framework. Further geometric structures, derived from other contrast functions strictly related to the Rényi entropy are explored and their link with the -geometry of Amari is highlighted., IOP
Journal of Physics A: Mathematical and Theoretical, 2020年03月18日, ［査読有り］ - On some information geometric structures concerning Mercator projections
Tatsuaki Wada, Elsevier
Physica A, 2019年10月01日, ［査読有り］ - On the canonical distributions of a thermal particle in a generalized velocity-dependent potential
T. Wada; A.M. Scarfone; H. Matsuzoe, Elsevior
Physica A, 2019年, ［査読有り］ - Normalization Problems for Deformed Exponential Families
H. Matsuzoe; A.M. Scarfone; T. Wada, Springer
Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science, vol 11712., 2019年, ［査読有り］ - Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies
Velimir M. Ilić; Antonio Maria Scarfone; Tatsuaki Wada, APS
Physical Review E, 2019年, ［査読有り］ - Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures
Antonio M. Scarfone; Hiroshi Matsuzoe; Tatsuaki Wada, MDPI
Entropy, 2018年06月05日, ［査読有り］, ［招待有り］ - Hessian-information geometric formulation of Hamiltonian systems and generalized Toda's dual transform
S. Goto; T. Wada
Journal of Physics A Mathematical and Theoretical, 2018年, ［査読有り］ - Conjugate Representations and Characterizing Escort Expectations in Information Geometry
Tatsuaki Wada; Hiroshi Matsuzoe, MDPI
Entropy, 2017年06月28日, ［査読有り］ - Composition law of kappa-entropy for statistically independent systems
G. Kaniadakis; A. M. Scarfone; A. Sparavigna; T. Wada, The intriguing and still open question concerning the composition law of kappa-entropy S-kappa(f) = 1/2 kappa Sigma(i) (f(i)(1-kappa) - f(i)(1+kappa) ) with 0 <kappa < 1 and Sigma(i) f(i) = 1 is here reconsidered and solved. It is shown that, for a statistical system described by the probability distribution f = {f(ij) }, made up of two statistically independent subsystems, described through the probability distributions p = {p(i)} and q = {q(j)}, respectively, with f(ij) = p(i)q(j), the joint entropy S-kappa(p q) can be obtained starting from the S-kappa(p) and S-kappa(q) entropies, and additionally from the entropic functionals S-kappa(p/e(kappa)) and S-kappa(q/e(kappa)), e(kappa) being the kappa-Napier number. The composition law of the kappa-entropy is given in closed form and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the kappa -> 0 limit., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2017年05月, ［査読有り］ - A Discrete Transmission Line Model for Discrete-time Quantum Walks
FUKUSHIMA Yusuke; WADA Tatsuaki, Graduate School of Information Sciences, Tohoku University
Interdisciplinary information sciences, 2017年03月31日, ［査読有り］, ［招待有り］ - A sequential structure of statistical manifolds on deformed exponential family
Hiroshi Matsuzoe; Antonio M. Scarfone; Tatsuaki Wada, Heavily tailed probability distributions are important objects in anomalous statistical physics. For such probability distributions, expectations do not exist in general. Therefore, an escort distribution and an escort expectation have been introduced. In this paper, by generalizing such escort distributions, a sequence of escort distributions is introduced. For a deformed exponential family, we study the fundamental properties of statistical manifold structures derived from the sequence of escort expectations., Springer Verlag
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2017年, ［査読有り］ - Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov-Nagumo average
A. M. Scarfone; H. Matsuzoe; T. Wada, We show the robustness of the structure of Legendre transforth in thermodynamics against the replacement of the standard linear average with the Kolmogorov-Nagumo nonlinear average to evaluate the expectation values of the macroscopic physical observables. The consequence of this statement is twofold: 1) the relationships between the expectation values and the corresponding Lagrange multipliers still hold in the present formalism; 2) the universality of the Gibbs equation as well as other thermodynamic relations are unaffected by the structure of the average used in the theory. (C) 2016 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
PHYSICS LETTERS A, 2016年09月, ［査読有り］ - Dualistic Hessian structure among the thermodynamic potentials in theκ-thermostatistics
T. Wada; H. Matsuzoe; A.M. Scarfone, We explore the information geometric structures among the thermodynamic potentials in the kappa-thermostatistics, which is a generalized thermostatistics based on the kappa-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the kappa-escort expectations and the other with the standard expectations. The associated kappa-generalized metrics are derived and related to the kappa-generalized fluctuation-response relations among the thermodynamic potentials in the kappa-thermostatistics., MDPI AG
Entropy, 2015年10月, ［査読有り］, ［招待有り］ - Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
Giuseppe Di Molfetta; Lauchlan Honter; Ben B. Luo; Tatsuaki Wada; Yutaka Shikano, Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schrödinger, massive Dirac, and Klein–Gordon equations. Here, two different types of Fibonacci discrete-time quantum walks are studied analytically. The first is the Fibonacci coin sequence with a generalized Hadamard coin and demonstrates six-step periodic dynamics. The other model is assumed to have three- or six-step periodic dynamics with the Fibonacci sequence. We analytically show that these models have ballistic transportation properties and continuous limits identical to those of the massless Dirac equation with coin basis change.
Quantum Studies: Mathematics and Foundations, 2015年09月, ［査読有り］ - Erratum to: Massless Dirac equation from Fibonacci discrete-time quantum walk
Giuseppe Di Molfetta; Lauchlan Honter; Ben B. Luo; Tatsuaki Wada; Yutaka Shikano
Quantum Studies: Mathematics and Foundations, 2015年09月, ［査読有り］ - Deformed Algebras and Generalizations of Independence on Deformed Exponential Families
Hiroshi Matsuzoe; Tatsuaki Wada, A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Though the deformed exponential families are defined by deformed exponential functions, these functions do not satisfy the law of exponents in general. The deformed algebras have been introduced based on the deformed exponential functions. In this paper, after summarizing such deformed algebraic structures, it is clarified how deformed algebras work on deformed exponential families. In fact, deformed algebras cause generalization of expectations. The three kinds of expectations for random variables are introduced in this paper, and it is discussed why these generalized expectations are natural from the viewpoint of information geometry. In addition, deformed algebras cause generalization of independences. Whereas it is difficult to check the well-definedness of deformed independence in general, the kappa-independence is always well-defined on kappa-exponential families. This is one of advantages of kappa-exponential families in complex systems. Consequently, we can well generalize the maximum likelihood method for the kappa-exponential family from the viewpoint of information geometry., MDPI AG
ENTROPY, 2015年08月, ［査読有り］, ［招待有り］ - Information Geometry on the κ-Thermostatistics
T. Wada; A.M. Scarfone, We explore the information geometric structure of the statistical manifold generated by the -deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fisher metric and affine connections. As a byproduct, we obtain the fluctuation-response relations in the -formalism based on the -generalized exponential family., MDPI AG
Entropy, 2015年03月, ［査読有り］, ［招待有り］ - 23pAH-3 フィボナッチ離散時間量子ウォークの数理
Molfetta Giuseppe Di; Honter Lauchlan; Luo Ben B.; 和田 達明; 鹿野 豊, 一般社団法人 日本物理学会
日本物理学会講演概要集, 2015年, ［査読有り］ - Legendre structure of kappa-thermostatistics revisited in the framework of information geometry
A. M. Scarfone; T. Wada, Information geometry is a powerful framework in which to study families of probability distributions or statistical models by applying differential geometric tools. It provides a useful framework for deriving many important structures in probability theory by identifying the space of probability distributions with a differentiable manifold endowed with a Riemannian metric. In this paper, we revisit some aspects concerning the kappa -thermostatistics based on the entropy S-kappa in the framework of information geometry. After introducing the dually flat structure associated with the kappa -distribution, we show that the dual potentials derived in the formalism of information geometry correspond to the generalized Massieu function Phi(kappa) and the generalized entropy S-kappa characterizing the Legendre structure of the kappa -deformed statistical mechanics. In addition, we obtain several quantities, such as escort distributions and canonical divergence, relevant for the further development of the theory., IOP PUBLISHING LTD
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014年07月, ［査読有り］ - Discrete-time quantum walk with feed-forward quantum coin
Yutaka Shikano; Tatsuaki Wada; Junsei Horikawa, Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a quantum-mechanical cellular automaton, a discrete-time quantum walk is defined to include various quantum dynamical behavior. Here we generalize a discrete-time quantum walk on a line into the feed-forward quantum coin model, which depends on the coin state of the previous step. We show that our proposed model has an anomalous slow diffusion characterized by the porous-medium equation, while the conventional discrete-time quantum walk model shows ballistic transport., NATURE PUBLISHING GROUP
SCIENTIFIC REPORTS, 2014年03月, ［査読有り］ - 30pAR-1 Nonlineax discrete-time quantum walk and anomalous diffusion
鹿野 豊; 和田 達明; 堀川 準世, 一般社団法人日本物理学会
日本物理学会講演概要集, 2014年, ［査読有り］ - The κ-Generalizations of Stirling Approximation and Multinominal Coefficients
T. Wada; H. Suyari, Stirling approximation of the factorials and multinominal coefficients are generalized based on the κ-generalized functions introduced by Kaniadakis. We have related the κ-generalized multinominal coefficients to the κ-entropy by introducing a new κ-product operation, which exists only when κ ≠ 0.
Entropy, 2013年12月, ［査読有り］ - Gau$\beta$原理と統計集団間の等価性を満たす一般化エントロピー (函数解析学による一般化エントロピーの新展開)
和田 達明, 京都大学
数理解析研究所講究録, 2013年09月, ［査読有り］, ［招待有り］ - Relationships between the Legendre structure in the $S_{2-q}$ formalism and the dually flat structure in the space of escort distributions
Tatsuaki Wada; Atsumi Ohara; Antonio M. Scarfone, We explore the relationships between the Legendre structure in the S2-q-formalism in nonextensive statistical mechanics and the dually-flat structure in information geometry. The q-generalized thermodynamic potentials in the S2-q-formalism are related to the dual potential functions in the information geometry., PERGAMON-ELSEVIER SCIENCE LTD
Reports on Mathematical Physics, 2012年, ［査読有り］ - The discrete-time quantum walk as a stochastic process in quantum mechanics
Yutaka Shikano; Junsei Horikawa; Tatsuaki Wada, Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete-time quantum walk (DTQW) has been experimentally realized in various setups. We show the limit distribution of the DTQW with the periodic position measurement under the time scale transformation and its connected to some physical-related models., IOP PUBLISHING LTD
Physica Scripta, 2012年, ［査読有り］ - Nonextensive entropies derived from Gauss’ principle
T. Wada, Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles. (C) 2011 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
Phys. Lett. A, 2011年, ［査読有り］ - Legendre duality and dually-flat structure in nonextensive thermostatistics developed by S_{2-q}-formalism
T. Wada; A. Ohara
Proceedings of Infromation Geometry and its Applications III, Aug. 02-06, University of Leipzig, Germany, 2010年08月, ［査読有り］ - A nonlinear drift which leads to κ-generalized distributions
T. Wada, We consider a system described by a Fokker-Planck equation with a new type of momentum-dependent drift coefficient which asymptotically decreases as -1/p for a large momentum p. It is shown that the steady-state of this system is a kappa-generalized Gaussian distribution, which is a non-Gaussian distribution with a power-law tail., SPRINGER
Eur. Phys. J. B, 2010年, ［査読有り］ - Information geometry of q-Gaussian densities and behaviors of solutions to related diffusion equations
A. Ohara; T. Wada
J. Phys. A: Math. Theor., 2010年, ［査読有り］ - Finite difference and averaging operators in generalized entropies
T. Wada; A.M. Scarfone, In the two-parameter generalization of thermostatistics based on the Sharma-Taneja-Mittal entropy not only the generalized entropic functional S a,b but also a new functional a,b plays a fundamental role. These functionals are related to the finite difference and averaging operators arising in finite difference calculus. © 2010 IOP Publishing Ltd., Institute of Physics Publishing
J. Phys.: Conf. Ser., 2010年, ［査読有り］ - Experimental investigation on the surface potential decays of dielectric materials with q-exponential function
J. Horikawa; T. Wada, We have studied the surface potential decays (SPD) of a variety of dielectric materials, and found that the SPD data of the samples with high charge retensions are well fitted by Tsallis q-exponential functions. © 2010 IOP Publishing Ltd., Institute of Physics Publishing
J. Phys.: Conf. Ser. 201, 2010年, ［査読有り］ - Gauss' law of error revisited in the framework of Sharma-Taneja-Mittal information measure
A.M. Scarfone; H. Suyari; T. Wada, We reformulate the Gauss' law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior., VERSITA
Cent. Eur. J. Phys., 2009年, ［査読有り］ - Lie symmetries and related group-invariant solutions of a nolinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy
A.M. Scarfone; T. Wada, In the framework of the statistical mechanics based on the Sharma-Taneja-Mittal entropy we derive a family of nonlinear Fokker-Planck equations characterized by the associated non-increasing Lyapunov functional. This class of equations describes kinetic processes in anomalous mediums where both super-diffusive and sub-diffusive mechanisms arise contemporarily and competitively. We classify the Lie symmetries and derive the corresponding group-invariant solutions for the physically meaningful Uhlenbeck-Ornstein process. For the purely diffusive process we show that any localized state asymptotically approaches a bell shape well fitted by a generalized Gaussian which is, in general, a quasi-self-similar solution for this class of purely diffusive equations., SOC BRASILEIRA FISICA
Braz. J. Phys., 2009年, ［査読有り］ - Asymptotic solutions of a nonlinear diffusive equation in the framework of \kappa-generalized statistical mechanics
T. Wada; A.M. Scarfone, The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the kappa-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the kappa-Gaussian function is not a scale invariant solution of the generalized diffusive equation. Notwithstanding, several numerical simulations, with different initial conditions, show that the solutions asymptotically approach to the kappa-Gaussian function. Simple argument based on a time-dependent transformation performed on the related kappa-generalized Fokker-Planck equation, supports this conclusion., SPRINGER
Eur. Phys. J. B, 2009年, ［査読有り］ - Generalized log-likelihood functions and Bregman divergences
T. Wada, Based on a two-parameter generalization of Gauss' law of error, a generalized log-likelihood is related to a Bregman divergence. This relation is a two-parameter generalization of the well-known relation between log-likelihood and Kullback-Leibler divergence. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257917], AMER INST PHYSICS
J. Math. Phys., 2009年, ［査読有り］ - A generalization of the log-likelihood function and weighted average in Gauss' law of error
Tatsuaki Wada; Hiroki Suyari, One of the promising approaches to how to derive a non-Gaussian distribution is generalizing the log-likelihood function in Gauss' law of error. In this contribution, it is shown that a generalization of the log-likelihood function in Gauss' law of error is equivalent to a generalization of the average. The proof is given for the case of the two-parameter generalized likelihood function, which unifies some known one-parameter generalizations., IEEE
2008 INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY AND ITS APPLICATIONS, VOLS 1-3, 2008年, ［査読有り］ - Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ,ν)-multinomial coefficient and Tsallis entropy Sq
H. Suyari; T. Wada, We derive the multiplicative duality "q <-> 1/q" and other typical mathematical structures as the special cases of the (mu, nu, q)-relation behind Tsallis statistics by means of the (mu, nu)-multinomial coefficient. Recently the additive duality "q <-> 2 - q" in Tsallis statistics is derived in the form of the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy. A slight generalization of this correspondence for the multiplicative duality requires the (mu, nu)-multinomial coefficient as a generalization of the q-multinomial coefficient. This combinatorial formalism provides us with the one-to-one correspondence between the (mu, nu)-multinomial coefficient and Tsallis entropy S-q, which determines a concrete relation among three parameters mu, nu and q, i.e., nu(1 - mu) + 1 = q which is called "(mu, nu, q)-relation" in this paper. As special cases of the (mu, nu, q)-relation, the additive duality and the multiplicative duality are recovered when nu = 1 and nu = q, respectively. As other special cases, when nu = 2 - q, a set of three parameters (mu, nu, q) is identified with the q-triplet (q(sen), q(rel), q(stat)) recently conjectured by Tsallis. Moreover, when nu = 1/q, the relation 1/(1 - q(sen)) = 1/alpha(min) - 1/alpha(max) in the multifractal singularity spectrum f (alpha) is recovered by means of the (mu, nu, q)-relation. (c) 2007 Published by Elsevier B.V., ELSEVIER SCIENCE BV
Phys. Lett. A, 2008年, ［査読有り］ - On the non-linear Fokker-Planck equation associated with \kappa-entropy
T. Wada and A.M. Scarfone, Based on the method developed in [T.D. Frank, Physica A 310 397-412 (2002)], we have derived a non-linear Fokker-Planck equation for non-equilibrium systems related to the kappa-entropy. This kinetic equation can be characterized by the associated Lyapunov functional or Bregman type divergence, which is related to the difference of the kappa-generalized free-energies., AMER INST PHYSICS
AIP conference proceedings, 2008年, ［査読有り］ - Equivalence among different formalisms in the Tsallis entropy framework
A. M. Scarfone; T. Wada, In a recent paper [T. Wada, A.M. Scarfone, Phys. Lett. A 335 (2005) 351] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend these results to a system which is out of equilibrium and evolves to a stationary state according to a nonlinear Fokker-Planck equation (NFPE). By means of time-scale conversion, it is shown that there exists a "correspondence" among the self-similar solutions of the NFPEs associated with the different Tsallis formalisms. The time-scale conversion is related to the corresponding Lyapunov functions of the respective NFPEs. (C) 2007 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007年10月, ［査読有り］ - On scaling law and Tsallis entropy derived from a fundamental nonlinear differential equation (非加法の数理と情報:函数解析の観点から RIMS研究集会報告集)
須鎗 弘樹; 和田 達明, 京都大学
数理解析研究所講究録, 2007年06月, ［査読有り］, ［招待有り］ - A two-parameter generalization of Shannon-Khinchin axioms and the uniqueness theorem
T. Wada; H. Suyari, Based on the one-parameter generalization of Shannon-Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sharma, Taneja, and Mittal. The corresponding unique theorem is also proved. It is found that our two-parameter generalization of Shannon additivity is a natural consequence from the Leibniz product rule of the two-parameter Chakrabarti-Jagannathan difference operator. (c) 2007 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
Phys. Lett. A, 2007年, ［査読有り］ - The Boltzmann temperature and Lagrange multiplier in nonextensive thermostatistics
Tatsuaki Wada; Antonio M. Scarfone, We consider the relation between the Boltzmann temperature and the Lagrange multipliers associated with energy average in the nonextensive thermostatistics. In Tsallis' canonical ensemble, the Boltzmann temperature depends on energy through the probability distribution unless q = 1. It is shown that the so-called 'physical temperature' introduced in [Phys. Lett. A 281 (2001), 126] is nothing but the ensemble average of the Boltzmann temperature., PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, 2006年, ［査読有り］ - Canonical Partition Function for Anomalous Systems Described by the κ-Entropy
Scarfone Antonio M; Wada Tatsuaki, Starting from the κ-distribution function, obtained by applying the maximal entropy principle to the κ-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical κ-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the κ-partition function. The relationship between the associated κ-free energy and the κ-entropy is also discussed., Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan
Progress of theoretical physics. Supplement, 2006年, ［査読有り］ - kappa-generalization of Gauss' law of error
Tatsuaki Wada; Hiroki Suyari, Based on the kappa-deformed functions (kappa-exponential and kappa-logarithm) and associated multiplication operation (kappa-product) introduced by Kaniadakis [Phys. Rev. E 66 (2002) 056125], we present another one-parameter generalization of Gauss' law of error. The likelihood function in Gauss' law of error is generalized by means of the K-product. This K-generalized maximum likelihood principle leads to the so-called kappa-Gaussian distributions. (c) 2005 Elsevier B.V All rights reserved., ELSEVIER SCIENCE BV
Phys. Lett. A, 2006年 - Connection between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy
Tatsuaki Wada; Antonio Maria Scarfone, Tsallis' thermostatistics with the standard linear average energy is revisited by employing S(2-q), which is the Tsallis entropy with q replaced by 2 - q. We explore the connections among the S(2-q) approach and the other different versions of Tsallis formalisms. It is shown that the normalized q-average energy and the standard linear average energy are related to each other. The relations among the Lagrange multipliers of the different versions are revealed. The relevant Legendre transform structures concerning the Lagrange multipliers associated with the normalization of probability are studied. It is shown that the generalized Massieu potential associated with S(2-q) and the linear average energy is related to one associated with the normalized Tsallis entropy and the normalized q-average energy. (C) 2004 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
Phys. Lett. A, 2005年 - A non self-referential expression of Tsallis' probability distribution function
Tatsuaki Wada; Antonio M. Scarfone, The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under either the linear mean energy constraint U or the escort mean energy constraint U(q) suffer self-referentiality. In a recent paper [Phys. Lett. A 335, 351 (2005)] the authors have shown that the pdfs obtained with either U or U(q) are equivalent to the pdf in a non self-referential form. Based on this result we derive an alternative expression for the Tsallis distributions, employing either U or U(q), which is non self-referential., SPRINGER
Eur. Phys. J B, 2005年, ［査読有り］ - Thermodynamic stability conditions for nonadditive composable entropies
T Wada, The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not equivalent to the corresponding TSC. It is shown that both the TSC of Tsallis' entropy and that of the kappa-generalized Boltzmann entropy are equivalent to the positivity of the standard heat capacity., SPRINGER-VERLAG
CONTINUUM MECHANICS AND THERMODYNAMICS, 2004年03月 - Thermodynamic stabilities of the generalized Boltzmann entropies
Tatsuaki Wada, We consider the thermodynamic stability conditions (TSC) on the Boltzmann entropies generalized by Tsallis' q- and KaniadakiS' kappa-deformed logarithmic functions. It is shown that the corresponding TSCs are not necessarily equivalent to the concavity of the generalized Boltzmann entropies with respect to internal energy. Nevertheless, both the TSCs are equivalent to the positivity of standard heat capacity. (C) 2004 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
Physica A, 2004年 - Model-free derivations of the Tsallis factor: constant heat capacity derivation
Tatsuaki Wada, The simple model-free derivations of the Boltzmann factor are extended by assuming the existence of an environment with a constant heat capacity in order to derive the Tsallis q-exponential factor, which reduces to the Boltzmann factor in the q --> I limit. It is shown that a constant of integration T-c in the constant heat capacity derivation is related with the nonintensive generalized temperature T-q, which is the thermal conjugate quantity of Tsallis' entropy S-q. (C) 2003 Elsevier B.V. All fights reserved., ELSEVIER SCIENCE BV
Physics Letter A, 2003年 - On the thermodynamic stability conditions of Tsallis' entropy
Tatsuaki Wada, The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw (Phys. Lett. A 198 (1995) 119) has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient to guarantee thermodynamic stability for all values of q due to the nonadditivity of Tsallis' entropy. Taking account of the nonadditivity the differential form of the TSC for Tsallis entropy is explicitly derived. It is shown that the resultant TSC for Tsallis' entropy is equivalent to the positivity of the standard specific heat. These results are consistent with the relation between Tsallis and Renyi entropies. (C) 2002 Elsevier Science B.V. All rights reserved., ELSEVIER SCIENCE BV
Physics Letter A, 2002年 - The additivity of the pseudo-additive conditional entropy for a proper Tsallis' entropic index
Tatsuaki Wada; Takeshi Saito, For Tsallis' entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value q* of the entropic index such that the asymptotic rate K-q drop lim(1-->infinity) (Sq(t) - S-q(0))/t of increase in S-q(t) remains finite whereas K-q vanishes (diverges) for q > q* (q < q*). We show that, in spite of the fact that the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions. the pseudo-additive conditional entropy S-q(t\0) drop (S-q(t) - S-q(0))/(1 + (1 - q)S-q(0)) becomes additive when q = q*. The connection between K-q* and the rate K-q*' drop S-q*(t\0)/t of increase in the conditional entropy is discussed. (C) 2002 Elsevier Science B.V. All rights reserved., ELSEVIER SCIENCE BV
Physica A, 2002年 - Interaction-round-a-face density-matrix renormalization-group method
T Wada; T Nishino, We demonstrate the numerical superiority of the interaction-round-a-face (IRF) density-matrix renormalization-group (DMRG) method applied to SU(2) invariant quantum spin chains over the conventional DMRG. The ground state energy densities and the gap energies of both S = 1 and S = 2 spin chains can be calculated using the IRF-DMRG without extensive computations. We have also studied the effect of tuning boundary interaction J(end) at both ends of the chain from the IRF view point. It is clearly observed that the magnon distribution is uniform when the best J(end) is chosen. (C) 2001 Elsevier Science B.V. All rights reserved., ELSEVIER SCIENCE BV
COMPUTER PHYSICS COMMUNICATIONS, 2001年12月 - When non-extensive entropy becomes extensive
Tatsuaki Wada; Takeshi Saito, Tsallis' non-extensive entropy S-q enables us to treat both power and exponential evolutions of underlying microscopic dynamics on an equal footing by adjusting the variable entropic index q to proper one q*. We propose an alternative constraint of obtaining the proper entropic index q* that the non-additive conditional entropy becomes additive if and only if q = q* in spite of the fact that the associated system cannot be decomposed into statistically independent subsystems. Long-range (time) correlation expressed by the q-exponential function is discussed based on the nature that the q-exponential function cannot be factorized into independent factors when q not equal 1. (C) 2001 Elsevier Science B.V. All rights reserved., ELSEVIER SCIENCE BV
Physica A, 2001年 - Interaction Round a Face DMRG method applied to rotational invariant quantum spin chains
Tatsuaki Wada, An interaction-round-a-face density-matrix renormalization-group (IRF-DMRG) method is developed for higher integer spin chain models which are rotational invariant. The expressions of the IRF weights associated with the nearest-neighbor spin-S interaction S-i. Si+1 are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps Delta and the ground state energy densities eo for both S = 1 and S = 2 isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only m = 90 states., AMERICAN PHYSICAL SOC
Physical Revew E, 2000年
MISC
- Generalized log-likelihood functions and Bregman divergences (vol 80, 113301, 2009)
Tatsuaki Wada
JOURNAL OF MATHEMATICAL PHYSICS, 2010年04月 - 24pPSA-27 反トンネル効果における量子の軌跡(24pPSA 領域11ポスターセッション,領域11(統計力学,物性基礎論,応用数学,力学,流体物理))
堀川 隼世; 和田 達明
日本物理学会講演概要集, 2010年 - Tsallis統計のマクロとミクロ—Macro and micro structures in Tsallis statistics—Non-commutative analysis and micro-macro duality
須鎗 弘樹; 和田 達明
数理解析研究所講究録, 2009年07月 - 30aPS-72 κ-Gauss分布を定常状態とする非線型ドリフト(30aPS 領域11ポスターセッション,領域11(統計力学,物性基礎論,応用数学,力学,流体物理))
和田 達明
日本物理学会講演概要集, 2009年 - 一般化熱統計学におけるLegendre構造--非線型Fokker-Planck方程式及びBregman divergenceとの関連—非可換解析とミクロ・マクロ双対性--RIMS研究集会報告集
和田 達明; Antonio M. Scarfone; 須鎗 弘樹
数理解析研究所講究録, 2008年07月 - 23aPS-72 κ-エントロピーに関する非線型拡散方程式(23aPS 領域11ポスターセッション,領域11(統計力学,物性基礎論,応用数学,力学,流体物理))
和田 達明
日本物理学会講演概要集, 2008年 - Geometric Aspects of a Certain Type of Nonlinear Diffusion Equations
A.Ohara; T. Wada
Proc. of the Int. Symp. on Nonlinear Theory and its Applications, 2008年 - トナー層における熱刺激電流(TSC)測定(2)—Thermally stimulated current measurements in toner layers (2)—日本画像学会年次大会(通算97回) Imaging Conference JAPAN 2006 論文集
小澤 修一; 竹内 学; 和田 達明
Imaging Conference Japan論文集, 2006年 - 非加法的統計力学--エントロピ(情報計量)のパラメータ拡張
和田 達明; Antonio M. Scarfone
電子情報通信学会技術研究報告 = IEICE technical report : 信学技報, 2005年12月16日 - 27aPS-52 K-deformed 指数及び対数関数に基づく統計力学(領域11,領域12合同ポスターセッション,領域11(統計力学,物性基礎論,応用数学,力学,流体物理))
和田 達明
日本物理学会講演概要集, 2005年
講演・口頭発表等
- 熱力学的過程と情報幾何における勾配流方程式
和田達明・A.M. Scarfone
日本物理学会2023春季大会, 2023年03月24日, 日本物理学会 - Geometry Colloquium: 情報幾何における勾配流方程式とHamilton方程式
和田 達明
北大数学 幾何学コロキウム, 2021年11月18日, 北大数学科
20211118, 20211118 - 非線型のRayleigh散逸関数と変形ガウス分布
和田達明
日本物理学会 秋季大会, 2019年09月11日 - 離散時間量子ウォークの伝送線路モデル
和田達明
日本物理学会 秋季大会, 2019年09月10日 - A discrete transmission line model which behaves like a DTQW
T. Wada; Y. Shikano
Workshop of Quantum Simulations and Quantum Walks, 2018年12月15日 - 30pAR-1 Nonlineax discrete-time quantum walk and anomalous diffusion
鹿野 豊; 和田 達明; 堀川 準世
日本物理学会講演概要集, 2014年, 一般社団法人日本物理学会 - Anomalous slow diffusion in nonlinear quantum walks
T. Wada; Y. Shikano; J. Horikawa
Workshop of Quantum Dynamics and Quantum Walks, 2012年11月24日, Yutaka Shikano (Institute of Molecular Science, Japan, Chair) Etsuo Segawa (Tohoku University, Japan) - Gauβ原理と統計集団間の等価性を満たす一般化エントロピ－
和田 達明
函数解析学による一般化エントロピ－の新展開, 2012年11月13日, 古一 茂 - A two-parameter representation of probability distributions and the associated divergence functions
T. Wada; A.M. Scarfone
International Workshop on Anomalous Statistics, Generalized Entropies, and Information Geometry (NEXT2012Nara), 2012年03月08日, Shun-ichi Amari (RIKEN, Japan), and Constantino Tsallis (CBPF, Brazil) Hiroki Suyari (Chiba Univ., Japan) chief organizer, Shigeru Furuichi (Nihon Univ., Japan), Atsumi Ohara (Univ. of Fukui, Japan), Yuzuru Sato (Hokkaido Univ., Japan), Mikito Tod - Legendre structure of κ-termostatistics: an information geometry approach
A.M. Scarfone; T. Wada
International Workshop on Anomalous Statistics, Generalized Entropies, and Information Geometry (NEXT2012Nara), 2012年03月06日, Shun-ichi Amari (RIKEN, Japan), and Constantino Tsallis (CBPF, Brazil) Hiroki Suyari (Chiba Univ., Japan) chief organizer, Shigeru Furuichi (Nihon Univ., Japan), Atsumi Ohara (Univ. of Fukui, Japan), Yuzuru Sato (Hokkaido Univ., Japan), Mikito Tod - 量子反射における量子軌跡
堀川 隼世; 和田 達明
基礎物理学研究所研究会,「物理と情報の階層構造 ―情報を接点とした諸階層の制御と創発―」, 2012年01月06日, 小嶋 泉 （京都大学 数理解析研究所）ほか - Legendre duality and dually-flat structure in nonextensive thermostatistics developed by S_{2-q} fomalism
T. Wada; A. Ohara
Conference on Information Geometry and its Application (IGIA3), 2010年08月02日, Max Planck institute for Mathematics in the Sciences - Finite difference and averaging operators in generalized entropies,
T. Wada; A.M. Scarfone
Kyoto-RIMS International Workshop "Mathematical Aspects of Generalized Entropies and their Applications", 2009年07月07日, 京都大学数理解析研究所（RIMS） - Asymptotic solutions of a nonlinear diffusive equation in the framework of \kappa-generalized statistical mechanics
T.Wada
International Conference in Statistical Physics, Crete, Greece, 2008年07月16日 - On the non-linear Fokker-Planck equation associated with \kappa-entropy
International conference on Complexity, Metastability and Nonextensivity, CTNEXT07, Catania, Italy, 1-5 July 2007, 2007年07月04日 - A two-parameter generalization of Shannon-Khinchin Axioms
和田 達明、須鎗 引樹
Conference on Complex Systems and Nonextensive Statistical Mechanics, 2006年08月07日
担当経験のある科目（授業）
共同研究・競争的資金等の研究課題
