Isomorph theory beyond thermal equilibrium

Area of Science:

• Statistical Mechanics
• Non-Equilibrium Systems
• Computational Physics

Background:

• Isomorph theory successfully describes equilibrium systems.
• Extending isomorph theory to non-equilibrium conditions is a significant challenge.
• Previous studies observed isomorph invariance in specific non-equilibrium scenarios.

Purpose of the Study:

• Generalize isomorph theory to systems far from thermal equilibrium.
• Introduce and define "systemic isomorphs" for non-equilibrium systems.
• Provide a unified theoretical framework for previously observed non-equilibrium isomorph invariance.

Main Methods:

• Definition of R-simple systems with hidden-scale-invariance.
• Introduction of "systemic temperature" and "systemic isomorphs."
• Analysis of dynamics invariance along systemic isomorphs based on temperature ratios.

Main Results:

• Generalization of isomorph theory to R-simple non-equilibrium systems.
• Identification of systemic isomorphs as lines of constant excess entropy.
• Demonstration of dynamics invariance under constant systemic-to-bath temperature ratios.
• Rationalization of isomorph invariance in shear flows, plastic flows, and glasses.

Conclusions:

• The proposed framework consistently explains isomorph invariance in diverse non-equilibrium systems.
• Systemic isomorphs offer a powerful tool for studying complex dynamics.
• Future work may involve redefining reduced quantities using systemic temperature.