Invariant quantities in shear flow

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.

4 pages, 2 figures

References in corpus (8)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Jamming, two-fluid behaviour and 'self-filtration' in concentrated particulate suspensions
• Rules for transition rates in nonequilibrium steady states
• Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems
• A possible classification of nonequilibrium steady states
• Detailed balance has a counterpart in non-equilibrium steady states
• Nonequilibrium Dynamics in Low Dimensional Systems
• Properties of a non-equilibrium heat bath

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