arXiv subjects

Kenshin Matsumoto

Publications and source records attributed to Kenshin Matsumoto.

3 recordsLinked to original sources

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Singularity of information flow at the Hopf bifurcation point

We investigate the singular behavior of information flow near the Hopf bifurcation point by analyzing the learning rate as a specific measure of information flow. We study the Brusselator, a model system exhibiting the Hopf bifurcation. We first numerically compute the learning rate in the stationary regime and find that it remains finite even in the deterministic limit, suggesting that the learning rate can be quantified in deterministic dynamics through probabilistic descriptions. Linear analysis accurately reproduces the numerical results in the stationary regime but fails near the bifurcation point. To overcome this limitation, we employ the singular perturbation method, well known in deterministic bifurcation theory, and carry out the corresponding calculation explicitly for a stochastic system described by a Langevin equation. This allows us to evaluate the learning rate near the bifurcation point. We then theoretically derive its non-smooth behavior in the deterministic limit. Our results demonstrate that changes in dynamical behavior are reflected in the learning rate and provide a basis for analyzing information processing in biochemical oscillations.

cond-mat.stat-mech↗

arXiv2025

Learning rate matrix and information-thermodynamic trade-off relation

Non-equilibrium systems exchange information in addition to energy. In information thermodynamics, the information flow is characterized by the learning rate, which is not invariant under coordinate transformations. To formalize the property of the learning rate under variable transformations, we introduce a learning rate matrix. This matrix has the learning rates as its diagonal elements and characterizes the changes in the learning rates under linear coordinate transformations. The maximal eigenvalue of the symmetric part of the learning rate matrix gives the maximal information flow under orthogonal transformations. Furthermore, we derive a new trade-off relation between the learning rate and the heat dissipation of a subsystem. Finally, we illustrate the results using analytically solvable yet experimentally feasible models.

cond-mat.stat-mech↗