Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes

TL;DR

This paper presents a comprehensive framework for understanding detailed balance in micro- and macrokinetics, emphasizing the importance of symmetry preservation and process distinguishability for maintaining detailed balance.

Contribution

It introduces two key conditions—symmetry preservation and process distinguishability—that are necessary for detailed balance to hold during micro-to-macro model reduction.

Findings

Equilibrium should not spontaneously break T- or PT-symmetry.

Macroscopic processes must be microscopically distinguishable.

Violations of these rules lead to breakdown of detailed balance.

Abstract

We develop a general framework for the discussion of detailed balance and analyse its microscopic background. We find that there should be two additions to the well-known $T$- or $PT$-invariance of the microscopic laws of motion: 1. Equilibrium should not spontaneously break the relevant $T$- or $PT$-symmetry. 2. The macroscopic processes should be microscopically distinguishable to guarantee persistence of detailed balance in the model reduction from micro- to macrokinetics. We briefly discuss examples of the violation of these rules and the corresponding violation of detailed balance.