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

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.

24 pages, 11 figures

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• Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Nonequilibrium thermodynamic potentials for continuous-time Markov chains
• Numerical comparison of a constrained path ensemble and a driven quasisteady state
• Enantiodromic effective generators of a Markov jump process with Gallavotti-Cohen symmetry
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?