Learning rate matrix and information-thermodynamic trade-off relation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916860217262080 |
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| 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 |
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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 |