Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Complex Systems Analysis

Background:

• Boundary-driven and out-of-equilibrium systems present challenges for stability analysis.
• Existing methods may be computationally intensive or lack a unified theoretical framework.

Purpose of the Study:

• To develop a novel stability analysis framework for non-equilibrium systems.
• To thermodynamically interpret the additivity principle and establish its validity conditions.
• To simplify the analysis of system stability, particularly for the weakly asymmetric exclusion process.

Main Methods:

• Hydrodynamic macroscopic fluctuation theory
• Hamiltonian description
• Cumulant generating function to derive a diagonal quadratic form
• Extension of the Le Chatelier principle

Main Results:

• A necessary and sufficient condition for the additivity principle's validity was derived.
• Stability conditions were linked to a diagonal quadratic form.
• A proof for the stability of the weakly asymmetric exclusion process was established.
• Stability analysis was reduced to solving two coupled linear ordinary differential equations.

Conclusions:

• The proposed framework offers a simplified and rigorous approach to stability analysis in non-equilibrium systems.
• The findings have potential applications in both classical and quantum systems.
• This work provides a new perspective on the Le Chatelier principle in the context of fluctuation theory.