Learning rate matrix and information-thermodynamic trade-off relation

Fuente: arXiv
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Main Authors: Matsumoto, Kenshin, Sasa, Shin-ichi, Dechant, Andreas
Format: Preprint
Published: 2025
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_version_ 1866916860217262080
author Matsumoto, Kenshin
Sasa, Shin-ichi
Dechant, Andreas
author_facet Matsumoto, Kenshin
Sasa, Shin-ichi
Dechant, Andreas
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_09981
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Learning rate matrix and information-thermodynamic trade-off relation
Matsumoto, Kenshin
Sasa, Shin-ichi
Dechant, Andreas
Statistical Mechanics
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.
title Learning rate matrix and information-thermodynamic trade-off relation
topic Statistical Mechanics
url https://arxiv.org/abs/2504.09981