Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics
Year: 2026
Type: preprint
Abstract: We investigate the relationship between the dissipation potential $S_{\mathrm{NB}}$ 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 $S_{\mathrm{NB}}$. Consequently, the local self-information is directly related to the dissipation potential, demonstrating that $S_{\mathrm{NB}}$ 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 $S_{\mathrm{NB}}$, 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.
Source: arXiv (Cornell University)
Authors: Katagiri, So, Wada, Tatsuaki
Institution: Ibaraki University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220655827