arXiv subjects

Koretaka Yuge

Publications and source records attributed to Koretaka Yuge.

At least 19 recordsLinked to original sources

arXiv2026

Unavoidable Canonical Nonlinearity Induced by Gaussian Measures Discretization

When we consider canonical averages for classical discrete systems, typically referred to as substitutional alloys, the map phi from many-body interatomic interactions to thermodynamic equilibrium configurations generally exhibits complicated nonlinearity. This canonical nonlinearity is fundamentally rooted in deviations of the discrete configurational density of states (CDOS) from continuous Gaussian families, and has conventionally been characterized by the Kullback-Leibler (KL) divergence on discrete statistical manifold. Thus, the previous works inevitablly missed intrinsic nonlinearities induced by discretization of Gaussian families, which remains invisible within conventional information-geometric descriptions. In the present work, we identify and quantify such unavoidable canonical nonlinearity by employing the specific transport cost W'2on the 2-Wasserstein framework with a cost function aligned with the Fisher metric for Gaussian families. We derive an explicit expression for this transport cost W'2 in the limit of vanishing discretization scale d to 0. We further show that this limiting Wasserstein distance admits a clear geometric interpretation on the statistical manifold, equivalent to a KL divergence associated with the expected parallel translations of continuous Gaussian. Our framework thus provides a transport-information-geometric characterization of discretization-induced nonlinearity in classical discrete systems. In addition, we confirm that this W'2-KL equivalence admits a natural generalization beyond Gaussian families. The correspondence reveals that the irreversible geometric distortion of the local measure induced by discretization, while extrinsic to information geometry alone, can generically be characterized by a standard KL divergence.

cond-mat.stat-mech↗

arXiv2026

Orthogonal Decomposition of Discretization-Induced Transport-Information Cost under Rank-Deficient Parametrizations

When we consider discretization of continuous probability distributions, it inevitably induces irreversible geometric distortion of local measure on the discretized support. While such discretziation-induced distortion is extrinsic to information geometry (IG) alone, we recently demonstrate that the discretization cost can be naturally characterized by the standard Kullback-Leibler (KL) divergence between continuous distributions as expectation of their infinitesimal parameter variations. The framework is based on the correspondence between optimal transport (OT) and IG, primarily requring the selected parameters directly identifiable with support coordinates. The present work extends the framework to more generalized parametrization theta, particularly the Jacobian between theta and support coordinates is rank-deficient, which generally results in breaking down the interpretation of the discretization-induced costs as information-geometric quantities. To address the problem, we here introduce an orthogonal decomposition of the second-moment tensor onto linear subspace for the covariance matrices generated by parameter fluctuations, based on Frobenius projection. The decomposition naturally separates the discretization cost into observable and unobservable components relative to the chosen parametrization. The present formulation provides a geometric framework for analyzing partial observability of discretization-induced transport-information costs. The present framework thus clarifies the role of parametrization-dependent information loss.

cond-mat.stat-mech↗

arXiv2026

Path-Integral Formulation of Unavoidable Canonical Nonlinearity: Dynamic Discretization Cost over Variable Supports

In the statistical thermodynamics of classical discrete systems, the map from microscopic interactions to thermodynamic equilibrium configurations generally exhibits complex nonlinearity, known as "canonical nonlinearity" (CN). While conventionally characterized by the Kullback-Leibler (KL) divergence, this approach inevitably misses intrinsic nonlinearities arising from the discretization of continuous Gaussian families themselves. This intrinsic effect of unavoidable CN (UCN), has recently been quantified within a transport-information-geometric framework. However, the UCN is fundamentally limited to evaluating the discretization-induced cost for a single continuous distribution. It therefore does not capture the information-geometric cost between a continuous Gaussian reference and an actual discrete distribution, nor between states with fundamentally different supports, making it conceptually unclear how to decompose the overall CN. To address this limitation, we propose the Path-Integral UCN (PUCN) quantifying the cumulative information-geometric cost between distinct distributions. The PUCN adopts a path by (i) retaining the canonical distribution as an exponential family via the $e$-mixture (geometric mean) of the base measure, leading to an arithmetic mixture of the Fisher metric as the CN standard, and (ii) enforcing covariant changes in the discretization cell through the harmonic mixture of its second-moment matrix $M$, reflecting the uncertainty in parameter variations on the statistical manifold. The resulting PUCN provides a flexible measure of the geometric cost between arbitrary states, including those with essentially different supports. This formulation enables an explicit quantification of CN between different CDOS systems and a natural decomposition of the total CN into the UCN and a residual contribution, which has not been clearly separated in existing approaches.

cond-mat.stat-mech↗

arXiv2025

Nonequilibrium Bounds for Canonical Nonlinearity Under Single-Shot Work

For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which is generally nonlinear. In terms of the configurational geometry (i.e., information about configurational density of states), the nonlinearity has been measured as special vector on configuration space, which is extended to Kullback-Leibler (KL) divergence on statistical manifold. Although they successfully provide new insight into how the geometry of lattice characterizes the nonlinearity, their application is essentially restricted to thermodynamic equilibrium. Based on the resource theory (especially, thermo-majorization), we here extend the applicability of the nonlinearity to nonequilibrium states obtained through single-shot work on Gibbs state. We reveal that the extended nonlinearity for nonequilibrium state is bounded from upper and lower by the information about one of the optimal Renyi divergences for equilibrium states in between practical and linear systems, and temperature and work.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic Approach for Nonlinearity within Canonical Ensemble

In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear relationship between a spectrum of many-body interactions and the corresponding equilibrium configuration, as determined through the canonical average. The proposed method facilitates the analysis of nonlinearity across multiple configurations via newly introduced thermodynamic functions. These functions enable the formulation of nonlinearity in the configuration space, previously conceptualized as local, and extend it to nonlocal nonlinearity within statistical manifolds. The present findings indicate that the average nonlinearity disparity between partially ordered and other configurations is constrained by the entropy production in an ideal linear system. This system is comprehensively described by a covariance matrix of the density of states in the configuration space. Practically, this approach could significantly advance the analysis of nonlinearity for various classical discrete systems.

cond-mat.stat-mech↗

arXiv2025

Geometric Study on Canonical Nonlinearity for FCC-based Binary Alloys

For classical discrete systems under constant composition (typically reffered to as substitutional alloys), canonical average can act as a map from a set of many-body interatomic interactions to that of configuration in thermodynamic equilibrium, the so-called canonical nonlinearity: CN, which generally exhibits complicated nonlinearity. Whereas our recent study reveals that the CN can be reasonablly addressed for individual microscopic configuration by two different measures of special vector field on configuration space2,3 and Kullback-Leibler (KL) divergence DKL, their direct correlation on real lattices, is still unclear. We here address this problem for fcc-based equiatomic binary alloys that have been one of the most studied system in the context of CN. We confirm that while local contribution to CN from DKL for each configuration exhibits strong, positive correlation with the vector field, non-local contribution from DKL exhibit no effective correlation. We find that depedence of the averaged non-local nonlinearity over all configurations can be well-characterized by normalied geometric distance in configurational polyhedra between for practical and separable system in terms of the structural degrees of freedom. This fact certainly indicates that non-local nonlinearity has profound connection to the geometric configuration for ground-state structures of alloys on configuration space.

cond-mat.stat-mech↗

arXiv2025

Structure Fluctuation Effects on Canonical-Nonlinear Thermodynamics

When we consider classical discrete systems under constant composition, their stable configuration in thermodynamic equilibrium can be typically obtained through the well-known canonica average phi. In configurational thermodynamics, phi as a map from many-body interatomic interaction to equilibrium configuration generally exhibits complicated nonlinearity, strongly depending on their underlying lattice. The connection between nonlinearity in phi (canonical nonlinearity) and the lattice has recently been amply investigated in terms of configurational geometry, leading to establishing its stochastic-thermodynamic treatment. The present work provides natural extention of the proposed treatment, explicitly including the effect of spatial fluctuation of the equilibrium configuration on thermodynamic property of the nonlinearity. We find that the fluctuation affects the upper-bound for the averaged nonlinearity disparity in multiple configurations, as an explicit and additional contribution from stochastic mutual information between focused coordination and its fluctuation, and an implicit contribution from changes in covariance matrix for density of states due to the fluctuation.

cond-mat.stat-mech↗

arXiv2025

Trends in Gibbs States for Thermodynamics of Canonical Nonlinearity

When we consider canonical average for classical discrete systems under constant composition (specifically, substitutional alloys) as a map phi from a set of many-body interatomic interactions to that of microscopic configuration in thermodynamic equilibrium, phi generally exhibits complicated nonlinearity. The nonlinearity has recently been amply studied in terms of configurational geometry, measured by vector field and Kullback-Leibler divergence, whose individual concepts are further unified through stochastic thermodynamic transformation: We call this procedure as Themodynamics of canonical nonlinearity (TCN). Although TCN can reveal the non-linear character across multiple configurations through thermodynamic functions, the essential role for Gibbs states (GBS) in terms of the nonlinearity is still totally unclear. We here tackle this problem, and reveal the characteristic roles of the GBS: (i) Concrete expression of the GBS is derived, (ii) strong correlation between GBSs and averaged nonlinearity over configurations for moled systems is found, and (iii) GBS-based bounds for averaged nonlinearity at specific conditions is derived.

cond-mat.stat-mech↗

arXiv2024

Geometric Study on Noncommutativity in Canonical Nonlinearity

For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in terms of configurational geometry, where two measures for the nonlinearity as vector field on configuration space and divergence on statistical manifold are introduced. Then, concepts of these measures are further unified through stochastic thermodynamic treatment. While these studies provide deeper insight into understanding the nonlinearity, thermodynamic treatment for non-separability in structural degrees of freedom (NS), still remains difficult due mainly to nonexistence of the corresponding CDOS. Our recent study partially overcome the problem, by considering additional information of non-commutativity for the nonlinearity (NC). The present study focuses on the basic behavior of the NC, in terms of the geometric information about configurational geometry, much more easily-accesible information than NC. For this purpose, we here employ the coarse-grained state model (CSM) that can qualitatively capture the nonlinearity information through the coarse-grained configuration space with tractable numbers of parameters, where the present CSM can implicitly include the difference in coordination numbers on real lattice. We find that (i) the NC exhibit positive correlation with asymmetric Hausdorff distance in configurational polyhedra between of pracitcal and separable systems in terms of SDFs, especially for partically-ordered-state-rich region, (ii) the NC take lower value when the difference in coordination number becomes small, indicating that we can obtain better thermodynamic bound for NS in such systems, and (iii) the positive correlation can be further modified when we additionally include information about nonseparability in the practical CDOS.

cond-mat.stat-mech↗

arXiv2024

Canonical Nonlinearity for Coupled Linear Systems

For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated nonlinearity (canonical nonlinearity). Our recent studies clarify that the nonlinearity can be reasonablly described both by specially-introduced vector field on configuration space and by corresponding diverngence on statistical manifold. While these studies shown that the correlation between vector field and local contribution to the divergence can be well characterized by coordination number for a set of selected structural degree of freedoms (SDFs), it is unclear whether the correlations between different set of SDFs purely comes from the difference in covariance matrix of CDOS (determined by coordination number) or additional information such as the shape of CP should be further required. To clarify the problem, we here propose simplified model of the so-called Coupled Linear System (CLS), which consists of the m-mixture of the configurational density of states for linear systems. We demonstrate that the CLS can reasonablly capture the changes in the local nonlinearity w.r.t. the changes in coordination number. Through the dynamic mode decomposition on CLS, we elucidate that there exists two dominant modes to capture the changes in the nonlinearity, where the one uniformly evolves from random to ordered configuration, and the another individually evolves around random, partially ordered and ordered configuration.

cond-mat.stat-mech↗

arXiv2023

Thermodynamic Interpretaion of Entanglement in Canonical Nonlinearity

For classical discrete system under constant composition, typically reffered to as substitutional alloys, canonical average acts as nonlinear map F from a set of potential energy surface U to that of microscopic configuration in thermodynamic equilibrium, Q, which is called canonical nonlinearity (CN). On statistical manifold, at any given configuration, F can be divided into the sum of local and non-local contribution in terms of Kullback-Leibler (KL) divergence, where the former has strong positive correlation with time evolution of the nonlinearity (NOL) on configuration space (called anharmonicity in structural degree of freedoms (ASDF), while the latter, corresponding to entanglement in SDFs, does exhibit clear correlation with the ASDF. On the other hand, our recent work bridge the different concepts of NOL on configuration space and statistical manifold through stochastic thermodynamics. While the work successfully provides clear relationships between the changes in total NOL through system transition and heat transfer, thermodynamic interpretation of how the entanglment in SDFs contributes to thermodynamic functions, is totally unclear due mainly to its non-trivial, non-local character. The present study tackle this problem, deriving upper bound for the entanglement for any given transition in terms of the mutual information, heat transfer and free energy. The present thermodynamic interpretaion will provide quantitative description of how the entanglement in SDFs is dominated by configuration of ground-state structures on configuration space.

cond-mat.stat-mech↗

arXiv2022

Thermodynamics for Nonlinearity under Hidden Structure Information

For substitutional alloys, typically refered to as classical discrete systems under constant composition, we theoretically examine the role of hidden structure information on evolution of nonlinearity (i.e., correspondence between a set of potential energy surface and that of many-body interaction) in canonical ensemble, in terms of the stochastic thermodynamics. When thermodynamic properties for a given paritial system is controlled by those for e.g., bulk as a hidden structure information, we derive that change in nonlinearity on statistical manifold through any transition is identical to the sum of negative bath entropy change, fluctuation of system entropy change and fluctuation of stochastic mutual information change between the system interested and hidden system: We successfully establish basic formulation of how geometric aspect of nonlinearity evolves under feedback from hidden system information, which especially provides deeper insight into the nonlinearity for surface and interface alloys controlled under bulk thermodynamics.

cond-mat.stat-mech↗

arXiv2021

Efficient, Systematic Estimation of Alloy Free Energy from Special Microscopic States

For classical discrete systems under constant composition typically refferred to substitutional alloys, we propose calculation method of Helmholtz free energy based on a set of special microscopic states. The advantage of the method is that configuration of the special states are essentially independent of energy and temperature, and they depend only on underlying lattice: The special states can be known a priori without any thermodynamic information, enabling systematic prediction of free energy for multicomponent alloys. We confirm that by comparing to conventional thermodynamic simulation, information about the special states provide reasonable predictive power above order-disorder and phase-separating transition temperature for alloys with many-body (up to 3-body) interactions.

cond-mat.stat-mech↗

arXiv2021

Tropical Diagram for Linear-Nonlinear Boundary in Canonical Ensemble

For classical discrete systems under constant composition, we re-examine how linear-nonlinear boundary in canonical ensemble, connecting a set of potential energy surface and that of microscopic configuration in thermodynamic equilibrium, is characterized by underlying lattice, from tropical geometry. We here show that by applying suitable tropical limit and multiple coordinate transform to time evolution of discrete dynamical system, reflecting geometric aspect of the nonlinearity, we successfully construct tropical diagram caputuring the universal character of linear/nonlinear region on configuration space for f = 2 structural degree of freedoms (SDFs). The diagram indicates that the boundary near disordered state is mainly dominated by constraints to individual SDF, while quasi linear-nonlinear boundary apart from disordered state is dominated by local non-separability in SDFs.

cond-mat.stat-mech↗

arXiv2021

Nonlinearity in Canonical Ensemble for Multicomponent Alloys Revisited from Structural Degree of Freedoms

For classical discrete system under constant composition typically referred to substitutional alloys, we examine local nonlinearity in canonical average phi . We have respectively investigated the local and global behavior of nonlinearity through previously-introduced vector field A and through tropical limit of the vector field. While these studies indicated the importance of constraints to structural degree of freedoms (SDFs) for global nonlinearity, it has been still unclear how the constraints to SDF affects local nonlinearity. Based on statistical manifold, we make intuitive bridge between the SDF-based information and local nonlinearity, decomposing the local nonlinearity into two (for binary alloys with pair correlations) or three (for otherwise) contributions in terms of the Kullback-Leibler divergence, where this decomposition is independent of temperature and many-body interaction, and is defined on individual configuration. We also find that we can provide A-dependent as well as A-independent decomposition of the local nonlinearity, where non-separability in SDFs and its nonadditive character is independent of A, which indicates that information about evolution of the vector field should be required to address the non-separability and nonadditivity. The present work enables to quantify how configuration-dependent constraints to SDF affect local nonlinearity in canonical average for multicomponent alloys.

cond-mat.stat-mech↗

arXiv2020

Tropical Limit for Configurational Geometry in Discrete Thermodynamic Systems

For classical discrete systems with constant composition (typically referred to substitutional alloys) under thermodynamically equilibrium state, macroscopic structure should in principle depend on temperature and many-body interaction through Boltzmann factor, exp(-bE). Despite this fact, our recently find that (i) thermodynamic average for structure can be characterized by a set of special microscopic state whose structure is independent of energy and temperature, and (ii) bidirectional-stability character for thermodynamic average between microscopic structure and potential energy surface is formulated without any information about temperature or many-body interaction. These results strongly indicates the significant role of configurational geometry, where anharmonicity in structural degree of freedom (ASDF) that is a vector field on configuration space, plays central role, intuitively corresponding to nonlinearity in thermodynamic average depending only on configurational geometry. Although ASDF can be practically drawn by performing numerical simulation based on such as Monte Carlo simulation, it is still unclear how its entire character is dominated by geometry of underlying lattice. We here show that by applying the limit in tropical geometry (i.e., tropical limit) with special scale-transformation to discrete dynamical system for ASDF, we find tropical relationships between how nonlinearity in terms of configurational geometry expands or shrinks and geometric information about underlying lattice for binary system with a single structural degree of freedom (SDF). The proposed tropical limit will be powerful procedure to simplify analyzation of complicated nonlinear character for thermodynamic average with multiple SDF systems.

cond-mat.stat-mech↗

arXiv2019

Universal Characterization of Hierarchical Ordering Tendency in High-Entropy Alloys from Configurational Geometry

Microscopic structures for fcc-based quaternary high-entropy alloys (HEA) in thermodynamically equilibrium state is examined based on first-principles (FP) calculation combined with our recently-developed theoretical approach. We find that (i) hierarchical ordering tendency for whole quaternary, and ternary and binary subsystems for the present five HEAs cannot be reasonably characterized by conventional Goldschmidt atomic radius or by those obtained from unary system for FP calculation, but can be systematically characterized by atomic radius from specially fluctuated configuration. (ii) ordering tendency for whole- and sub-systems can be simultaneously treated with individual definition of atomic radius ratio, and that linear correlation between ordering tendency and atomic radius ratio naturally decreases with decrease of number of constituents for whole (or sub-) system due to the counterbalance breaking of like- and unlike-atom neighboring pair. We also find that by introducing appropriate normalization, ordering tendency for systems with different number of constituents (here, quaternary and ternary) can also be simultaneously treated by the atomic radius ratio.

cond-mat.mtrl-sci↗

arXiv2019

Optimal Selection of Structural Degree of Freedoms for Spceial Microscopic States to Characterize Disordered Structures

For classical discrete systems under constant composition, statistical mechanics tells us that a set of microscopic state dominantly contributing to thermodynamically equilibrium state should depend on temperature as well as on many-body interaction (i.e. thermodynamic information), through Boltzamann factor of exp(-bE). Despite this fact, our recent study reveals that a single (and a few additional) microscopic state (called projection state: PS), whose structure can be known a priori without r equiring thermodynamic information, can universally characterize equiibrium properties for disordered states, where their sturctures depends on configurational geometry before applying many-body interaction to the system. Although mathematical condition for the structures of PS have been rigorously established, practically effective condition for constructing the stuructures, especially for which set of a finite structural degree of freedoms (SDF) should be selected for considered coordination has not been clarified so far. We here tuckle this problem, proposing a quantitative and systematic criteria for an optimal set of SDFs. The present proposal enables to effectively constructing PSs for a limited system size, and also providing new insight into which set of SDFs should generally affects equilibrium properties along a chosen coordination, without using any thermodynamic information.

cond-mat.stat-mech↗