arXiv subjects

Akihisa Ichiki

Publications and source records attributed to Akihisa Ichiki.

15 recordsLinked to original sources

arXiv2026

Relativity of Observation: Operational Intensive Variables in Nonequilibrium Thermodynamics

We formulate nonequilibrium thermodynamics in which intensive variables acquire operational meaning through measurement protocols consistent with local reciprocity. Using physical equilibrium as a reference, conjugate observables are constructed by continuously adjusting devices along the local tangent space of the statistical manifold. In this relativity of observation, Onsager reciprocity holds locally, allowing inference-based Lagrange multipliers to be directly measured. This provides a systematic method to extend operational definitions of intensive variables to nonequilibrium states, highlighting their context-dependent nature and offering a concrete experimental strategy.

cond-mat.stat-mech↗

arXiv2026

Inferring Microscopic Explanatory Structures from Observational Constraints via Large Deviations

We study how macroscopic observational constraints restrict admissible microscopic explanatory structures when no intrinsic order or dynamics is assumed a priori. Starting from an unordered collection of measurement outcomes, we formulate inference as a constrained large deviation problem, selecting probability assignments that minimize relative entropy with respect to a reference measure determined solely by the measurement setup. We show that among all microscopic structures compatible with a given macroscopic constraint, those rendering the observation statistically most typical are selected. As an explicit illustration, we demonstrate how ordered microscopic structures can emerge purely from inference under constraint, even when the reference measure is fully permutation symmetric. Order is thus not assumed but inferred, serving here only as an illustrative example of a broader class of relational explanatory hypotheses constrained by observation.

cond-mat.stat-mech↗

arXiv2025

A method for classification of data with uncertainty using hypothesis testing

Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that belong to overlapping regions of the two class distributions or for data outside the distributions (out-of-distribution data). Therefore, conventional classifiers should not be applied in high-risk fields where classification results can have significant consequences. In order to address this issue, it is necessary to quantify uncertainty and adopt decision-making approaches that take it into account. Many methods have been proposed for this purpose; however, implementing these methods often requires performing resampling, improving the structure or performance of models, and optimizing the thresholds of classifiers. We propose a new decision-making approach using two types of hypothesis testing. This method is capable of detecting ambiguous data that belong to the overlapping regions of two class distributions, as well as out-of-distribution data that are not included in the training data distribution. In addition, we quantify uncertainty using the empirical distribution of feature values derived from the training data obtained through the trained model. The classification threshold is determined by the $α$-quantile and ($1-α$)-quantile, where the significance level $α$ is set according to each specific situation.

cs.LG↗

arXiv2023

Performance-guaranteed regularization in maximum likelihood method: Gauge symmetry in Kullback -- Leibler divergence

The maximum likelihood method is the best-known method for estimating the probabilities behind the data. However, the conventional method obtains the probability model closest to the empirical distribution, resulting in overfitting. Then regularization methods prevent the model from being excessively close to the wrong probability, but little is known systematically about their performance. The idea of regularization is similar to error-correcting codes, which obtain optimal decoding by mixing suboptimal solutions with an incorrectly received code. The optimal decoding in error-correcting codes is achieved based on gauge symmetry. We propose a theoretically guaranteed regularization in the maximum likelihood method by focusing on a gauge symmetry in Kullback -- Leibler divergence. In our approach, we obtain the optimal model without the need to search for hyperparameters frequently appearing in regularization.

stat.ML↗

arXiv2021

Stochastic dynamics without detailed balance condition connecting simple gradient method and Hamiltonian Monte Carlo

Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the acceleration of convergence to the target distribution. Hamiltonian Monte Carlo (HMC) is such a variant of MCMC. In the recent development of MCMC, another approach based on the violation of the detailed balance condition has attracted much attention. Historically, these two approaches have been proposed independently, and their relationship has not been clearly understood. In this paper, the two approaches are seamlessly understood in the framework of generalized Monte Carlo method that violates the detailed balance condition. Furthermore we propose an efficient Monte Carlo method based on our framework.

cond-mat.stat-mech↗

arXiv2021

Upper bound inequality for calculation time in simulated annealing analogous to adiabatic theorem in quantum systems

It has been recently reported that classical systems have speed limit for state evolution, although such a concept of speed limit had been considered to be unique to quantum systems. Owing to the speed limit for classical system, the lower bound for calculation time of simulated annealing with desired calculation accuracy can be derived. However, such a lower bound does not work as a criterion for completion of calculation in a practical time. In this paper, we derive an inequality for classical system analogous to the quantum adiabatic theorem that gives calculation time for an accuracy-guaranteed fluctuation-exploiting computation. The trade-off relation between calculation time and accuracy is given in the form tolerable in practical use.

quant-ph↗

arXiv2020

Diversity of dynamical behaviors due to initial conditions: exact results with extended Ott--Antonsen ansatz for identical Kuramoto--Sakaguchi phase oscillators

The Ott--Antonsen ansatz is a powerful tool to extract the behaviors of coupled phase oscillators, but it imposes a strong restriction on the initial condition. Herein, a systematic extension of the Ott--Antonsen ansatz is proposed to relax the restriction, enabling the systematic approximation of the behavior of a globally coupled phase oscillator system with an arbitrary initial condition. The proposed method is validated on the Kuramoto--Sakaguchi model of identical phase oscillators. The method yields cluster and chimera-like solutions that are not obtained by the conventional ansatz.

nlin.AO↗

arXiv2019

Chaotic synchronization induced by external noise in coupled limit cycle oscillators

A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely coupled oscillators is derived without any approximation through an analysis based on the nonlinear Fokker--Planck equation. Chaotic synchronization associated with the appearance of macroscopic chaotic behavior is shown by investigating the changes in averaged motion with increasing noise intensity.

nlin.CD↗

arXiv2015

Langevin dynamics neglecting detailed balance condition

An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann distribution involve numerical simulations under the detailed balance condition. In contrast, in the present study we formulate the Langevin dynamics, for which the corresponding Fokker-Planck operator includes an asymmetric component violating the detailed balance condition. This leads to shifts in the eigenvalues and results in the acceleration of the relaxation toward the steady state. The numerical implementation demonstrates faster convergence and shorter correlation time, and the technique of biased event sampling, Nemoto-Sasa theory, further highlights the efficacy of our method.

cond-mat.stat-mech↗

arXiv2015

Full-order fluctuation-dissipation relation for a class of non-equilibrium steady states

Acceleration of relaxation toward a fixed stationary distribution via violation of detailed balance was reported in the context of a Markov chain Monte Carlo method recently. Inspired by this result, systematic methods to violate detailed balance in Langevin dynamics were formulated by using exponential and rotational nonconservative forces. In the present paper, we accentuate that such specific nonconservative forces relate to the large deviation of total heat in an equilibrium state. The response to these nonconservative forces can be described by the intrinsic fluctuation of the total heat in the equilibrium state. Consequently, the fluctuation-dissipation relation for nonequilibrium steady states is derived without recourse to a linear response approximation.

cond-mat.stat-mech↗

arXiv2013

Violation of detailed balance accelerates relaxation

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.

cond-mat.stat-mech↗

arXiv2013

Singular probability distribution of shot-noise driven systems

We study the stationary probability distribution of a system driven by shot noise. We find that, both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For sufficiently low rate of noise pulses they correspond to distribution peaks. We find the positions of the peaks and the corresponding exponents. In the underdamped regime the peak positions are given by a geometric progression. The energy distribution in this case also displays multiple peaks with positions given by a geometric progression. Such structure is a signature of the shot-noise induced fluctuations. The analytical results are in excellent agreement with numerical simulations.

cond-mat.mes-hall↗

arXiv2009

Phase transitions driven by Lévy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of Lévy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with Lévy noise have attracted much attention and behaviors of systems with double-well potential subjected to Lévy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an {\it analytically solvable model} to study the occurrence of phase transitions driven by Lévy stable noise.

cond-mat.stat-mech↗

arXiv2007

Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise

Effects of synaptic noise on the retrieval process of associative memory neural networks are studied from the viewpoint of neurobiological and biophysical understanding of information processing in the brain. We investigate the statistical mechanical properties of stochastic analog neural networks with temporally fluctuating synaptic noise, which is assumed to be white noise. Such networks, in general, defy the use of the replica method, since they have no energy concept. The self-consistent signal-to-noise analysis (SCSNA), which is an alternative to the replica method for deriving a set of order parameter equations, requires no energy concept and thus becomes available in studying networks without energy functions. Applying the SCSNA to stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP) equation which defines the deterministic networks equivalent to the original stochastic ones. The study of the TAP equation which is of particular interest for the case without energy concept is very few, while it is closely related to the SCSNA in the case with energy concept. This paper aims to derive the TAP equation for networks with synaptic noise together with a set of order parameter equations by a hybrid use of the cavity method and the SCSNA.

cond-mat.dis-nn↗

arXiv2006

Thouless-Anderson-Palmer equation and self-consistent signal-to-noise analysis for the Hopfield model with three-body interaction

The self-consistent signal-to-noise analysis (SCSNA) is an alternative to the replica method for deriving the set of order parameter equations for associative memory neural network models and is closely related with the Thouless-Anderson-Palmer equation (TAP) approach. In the recent paper by Shiino and Yamana the Onsager reaction term of the TAP equation has been found to be obtained from the SCSNA for Hopfield neural networks with 2-body interaction. We study the TAP equation for an associative memory stochastic analog neural network with 3-body interaction to investigate the structure of the Onsager reaction term, in connection with the term proportional to the output characteristic to the SCSNA. We report the SCSNA framework for analog networks with 3-body interactions as well as a novel recipe based on the cavity concept that involves two cavities and the hybrid use of the SCSNA to obtain the TAP equation.

cond-mat.dis-nn↗