On the statistical physics of metastable and non-equilibrium stationary states

TL;DR

This paper extends the statistical physics framework to describe metastable and non-equilibrium states using a modified Gibbs scheme, revealing a connection to Tsallis entropy and providing a basis for analyzing complex systems.

Contribution

It introduces a new statistical approach incorporating additional dynamical constraints, linking metastable states to Tsallis entropy and eigenvalue distributions.

Findings

Eigenvalues of constraint operators follow a Tsallis structure.

Metastable states are characterized by a homogeneous dependence on the density matrix.

The approach bridges non-equilibrium states with generalized entropy frameworks.

Abstract

The optimization problems defining meta-stable or stationary equilibrium are explored. The Gibbs scheme is modified aiming to describe the statistical properties of a class of non-equilibrium and metastable states. The system is assumed to maximize the usual definition of the Entropy, subject to the standard constant energy and norm restrictions, plus additional constraints. The central assumption is that the existence of the considered metastable state is determined by the action of this additional dynamical constraint, that blocks the evolution of the system up to its maximum Entropy state, thus maintaining it in the metastable or stationary configuration. After requiring from the statistical description to be valid for the combination of two nearly independent subsystems, it follows that the eigenvalues of the constraint operators C should have the restricted homogeneous form C(p{i})=p{i}^{q}, in terms of the eigenvalues of the density matrix p{i}, where q is a fixed real number. Therefore, the distribution of the eigenvalues of the constraint function have the Tsallis structure. This conclusion suggests the interpretation of the q parameter as reflecting the homogeneous dependence of the constraint determining the metastable state on the density matrix. An application to the plasma experiments of Huang and Driscoll is expected to be considered elsewhere in order to compare the results with Tsallis scheme and the minimal Enstrophy one.