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Tatsuaki Wada

Publications and source records attributed to Tatsuaki Wada.

At least 19 recordsLinked to original sources
arXiv2026

Reframing of Information Geometry via Symmetric Teleparallel Gravity

Information geometry has traditionally been formulated within the framework of Riemannian geometry and dual affine connections. This work aims to reframe the foundational structure of information geometry by introducing the geometric machinery of symmetric teleparallel gravity. By requiring both curvature and torsion to vanish globally on the statistical manifold, it is demonstrated that the fundamental properties of the information space can be entirely encoded in the non-metricity tensor. This approach clarifies the distinction between the general $ξ$-parameterized case and the $θ$- or $η$-parameterized cases, which correspond to general symmetric teleparallel gravity and its coincident gauge, respectively. Specifically, the $θ$- or $η$-coordinates emerge as special coordinates in the coincident gauge, where the connection coefficients vanish.

gr-qc↗
arXiv2025

Weyl symmetry of the gradient-flow in information geometry

We have revisited the gradient-flow in information geometry from the perspective of Weyl symmetry. The gradient-flow equations are derived from the proposed action which is invariant under the Weyl's gauge transformations. In Weyl integrable geometry, we have related Amari's $α$-connections in IG to the Weyl invariant connection on the Riemannian manifold equipped with the scaled metric.

gr-qc↗
arXiv2023

Mechanics of geodesics in Information geometry and Black Hole Thermodynamics

In this article 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.

cs.IT↗
arXiv2023

Huygens' equations and the gradient-flow equations in information geometry

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 $\textit{t}$ 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, it is found the relation between the gradient-flow equation and replicator equations.

cs.IT↗
arXiv2023

A Weyl geometric approach to the gradient-flow equations in information geometry

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.

math-ph↗
arXiv2023

On the Kaniadakis distributions applied in statistical physics and natural sciences

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.

cond-mat.stat-mech↗
arXiv2020

The k-statistics approach to epidemiology

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $κ$-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $κ$-statistics in fitting empirical data. In this paper, we use $κ$-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $κ$-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $κ$-Weibull model has universal features.

q-bio.PE↗
arXiv2019

On the equivalence between four versions of thermostatistics based on strongly pseudo-additive entropies

The class of SPA entropies, which can be represented as an increasing continuous transformation of Shannon and Rényi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been explored and established by GSK axioms, the analysis of their thermostatistical properties have mostly been limited to special cases which belong to two parameter Sharma-Mittal entropy class, such as Tsallis, Renyi and Gaussian entropies. In this paper we present a general analysis of SPA entropies thermostatistics by taking into account both linear and escort constraints on internal energy. We develop two types of dualities between the thermostatistics formalisms. By the first one, the formalism of Rényi entropy is transformed in the formalism of SPA entropy under general energy constraint and, by the second one, the generalized thermostatistics which corresponds to the linear constraint is transformed into the one which corresponds to the escort constraint. Thus, we establish the equivalence between four different thermostatistics formalisms based on Rényi and SPA entropies coupled with linear and escort constraints and we provide the transformation formulas. In this way we obtain a general framework which is applicable to the wide class of entropies and constraints previously discussed in the literature. As an example, we rederive maximum entropy distributions for Sharma-Mittal entropy and we establish new relationships between the corresponding thermodynamic potentials. We obtain, as special cases, previously developed expressions for maximum entropy distributions and thermodynamic quantities for Tsallis, Rényi and Gaussian entropies. In addition, the results are applied for derivation of thermostatistical relationships for supra-extensive entropy, which has not previously been considered.

math-ph↗
arXiv2019

On the canonical distributions of a thermal particle in the weakly confining potential of special type

We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state of the Fokker-Planck equation is shown to be a canonical probability distribution. Furthermore an appropriate re-parametrization relates this stationary state with the $κ$-deformed Gaussian.

cond-mat.stat-mech↗
arXiv2019

On some information geometric structures concerning Mercator projections

Some information geometric structures concerning the Mercator projections are studied. It is known that a loxodrome on the surface of the globe is related to the straight line on a Mercator map by the Mercator projection. It is not well known that an affine connection with torsion plays a fundamental role to describe an auto-parallel path on the surface. Based on these information geometric structures, Gauss distribution is reconsidered from the view point of the affine connection with a torsion. Some relations with deformed functions are also pointed out.

math.GM↗
arXiv2018

Hessian-information geometric formulation of Hamiltonian systems and generalized Toda's dual transform

In this paper a class of classical Hamiltonian systems is geometrically formulated. This class is such that a Hamiltonian can be written as the sum of a kinetic energy function and a potential energy function. In addition, these energy functions are assumed strictly convex. For this class of Hamiltonian systems Hessian and information geometric formulation is given. With this formulation, a generalized Toda's dual transform is proposed, where his original transform was used in deriving his integrable lattice system. Then a relation between the generalized Toda's dual transform and the Legendre transform of a class of potential energy functions is shown. As an extension of this formulation, dissipation-less electric circuit models are also discussed in the geometric viewpoint above.

math-ph↗
arXiv2014

Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk

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.

quant-ph↗
arXiv2014

Discrete-time quantum walk with feed-forward quantum coin

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.

quant-ph↗
arXiv2009

Information Geometry of q-Gaussian Densities and Behaviors of Solutions to Related Diffusion Equations

This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure with information geometry on the manifold of generalized exponential densities. Next by considering such a structure in particular on the q-Gaussian densities, we derive several physically and geometrically interesting properties of the solutions. They include, for example, characterization of the moment-conserving projection of a solution, evaluation of evolutional velocities of the second moments and the convergence rate to the manifold in terms of the geodesic curves, divergence and so on.

cond-mat.stat-mech↗
arXiv2009

A nonlinear drift which leads to $κ$-generalized distributions

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 $κ$-generalized Gaussian distribution, which is a non-Gaussian distribution with a power-law tail.

cond-mat.stat-mech↗