Invariant quantities in shear flow

TL;DR

This paper derives universal invariant quantities for nonequilibrium steady states in shear-driven systems, providing exact relations that hold far from equilibrium and facilitate transition rate calculations.

Contribution

It introduces a set of simple, exact invariant quantities for driven steady states based on a nonequilibrium counterpart to detailed balance.

Findings

Invariant quantities remain unchanged under driving conditions.

Relations are exact and valid far from equilibrium.

Enable systematic calculation of transition rates in complex systems.

Abstract

The dynamics of systems out of thermal equilibrium is usually treated on a case-by-case basis without knowledge of fundamental and universal principles. We address this problem for a class of driven steady states, namely those mechanically driven at the boundaries such as complex fluids under shear. From a nonequilibrium counterpart to detailed balance (NCDB) we derive a remarkably simple set of invariant quantities which remain unchanged when the system is driven. These new nonequilibrium relations are both exact and valid arbitrarily far from equilibrium. Furthermore, they enable the systematic calculation of transition rates in driven systems with state-spaces of arbitrary connectivity.