Nonlinear Dynamical Equation for Irreversible, Steepest-Entropy-Ascent Relaxation to Stable Equilibrium

TL;DR

This paper explores a nonlinear evolution equation in Quantum Thermodynamics that models irreversible relaxation to equilibrium, emphasizing its mathematical structure and broad applicability across physics and information theory.

Contribution

It introduces a nonlinear dynamical law that uniquely describes irreversible relaxation, satisfying thermodynamic stability and applicable to various physical and informational systems.

Findings

Provides a deterministic description of relaxation to equilibrium.

Ensures stability consistent with the second law of thermodynamics.

Applicable to both classical and quantum systems.

Abstract

We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group providing a unique deterministic description of irreversible, conservative relaxation towards equilibrium from any non-equilibrium state, and satisfies a very restrictive stability requirement equivalent to Hatsopoulos-Keenan statement of the second law of thermodynamics. Here, we emphasize its mathematical structure and its applicability also within other contexts, such as Classical and Quantum Statistical Mechanics, and Information Theory.