Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations

TL;DR

This paper explores how shear flow influences microscopic dynamics in complex fluids, revealing invariant transition rate relations and a fluctuation theorem, thereby advancing understanding of nonequilibrium steady states.

Contribution

It provides a detailed, pedagogical account of invariant quantities and the nonequilibrium detailed balance, linking transition rates to shear currents in steady states.

Findings

Invariant transition rate relations under shear flow

Existence of a Gallavotti-Cohen type fluctuation relation

Connection between microscopic dynamics and macroscopic shear current

Abstract

In modeling nonequilibrium systems one usually starts with a definition of the microscopic dynamics, e.g., in terms of transition rates, and then derives the resulting macroscopic behavior. We address the inverse question for a class of steady state systems, namely complex fluids under continuous shear flow: how does an externally imposed shear current affect the microscopic dynamics of the fluid? The answer can be formulated in the form of invariant quantities, exact relations for the transition rates in the nonequilibrium steady state, as discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett. 101, 240601 (2008)]. Here, we present a more pedagogical account of the invariant quantities and the theory underlying them, known as the nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we investigate the relationship between the transition rates and the shear current in the steady state. We show that a fluctuation relation of the Gallavotti-Cohen type holds for systems satisfying NCDB.