Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics
Abstract
We investigate the relationship between the dissipation potential SNB and information entropy in stochastic Nambu nonequilibrium thermodynamics (NNET). Starting from pure diffusion, gradient-flow systems, and systems with Hamiltonian rotational currents, we derive the stationary distribution of the Fokker--Planck equation including a Nambu flow. We show that, when the Nambu flow preserves the dissipation potential and an Einstein-type relation holds between the diffusion matrix and the transport tensor, the stationary distribution is governed by an exponential weight determined by SNB. Consequently, the local self-information is directly related to the dissipation potential, demonstrating that SNB should not be identified with the Shannon entropy itself but instead serves as the stationary quasipotential governing the nonequilibrium steady-state distribution. Using the distinction between the thermodynamic entropy and the dissipation potential established for an open gas--piston system coupled to a thermal bath and an external-pressure reservoir, we further clarify the Massieu interpretation of SNB, introduce a Nambu canonical distribution, and derive the covariance of fluctuations within the saddle-point approximation. These results provide a statistical interpretation of the NNET dissipation potential by identifying it as the stationary quasipotential underlying nonequilibrium steady states.
Related
- Nonequilibrium distribution for stochastic thermodynamics
- Nonequilibrium stochastic thermodynamics of boundary functionals: From Zubarev's ensemble to stochastic particle separation
- Nonequilibrium Thermodynamics of Semilinear Stochastic Partial Differential Equations
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- Nambu Nonequilibrium Thermodynamics and the Lyapunov Structure of Open Systems
BibTeX
@misc{katagiri2026information,
title = {{Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics}},
author = {So Katagiri and Tatsuaki Wada},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03790},
eprint = {2610.03790},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03790},
}
RIS
TY - UNPB
TI - Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics
AU - So Katagiri
AU - Tatsuaki Wada
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03790
UR - https://arxiv.org/abs/2610.03790
AB - We investigate the relationship between the dissipation potential S_NB and information entropy in stochastic Nambu nonequilibrium thermodynamics (NNET). Starting from pure diffusion, gradient-flow systems, and systems with Hamiltonian rotational currents, we derive the stationary distribution of the Fokker--Planck equation including a Nambu flow. We show that, when the Nambu flow preserves the dissipation potential and an Einstein-type relation holds between the diffusion matrix and the transport tensor, the stationary distribution is governed by an exponential weight determined by S_NB. Consequently, the local self-information is directly related to the dissipation potential, demonstrating that S_NB should not be identified with the Shannon entropy itself but instead serves as the stationary quasipotential governing the nonequilibrium steady-state distribution. Using the distinction between the thermodynamic entropy and the dissipation potential established for an open gas--piston system coupled to a thermal bath and an external-pressure reservoir, we further clarify the Massieu interpretation of S_NB, introduce a Nambu canonical distribution, and derive the covariance of fluctuations within the saddle-point approximation. These results provide a statistical interpretation of the NNET dissipation potential by identifying it as the stationary quasipotential underlying nonequilibrium steady states.
ER -