Work, work fluctuations, and the work distribution in a thermal non-equilibrium steady state

TL;DR

This paper investigates the properties of work fluctuations and distributions in non-equilibrium steady states caused by temperature gradients, highlighting their anomalous nature and differences from equilibrium systems.

Contribution

It introduces the concept of non-equilibrium Casimir work, proposes a new measurement approach, and analyzes the distinct work fluctuations and distributions in long-range correlated systems.

Findings

Non-equilibrium work fluctuations are highly anomalous.

The non-equilibrium work distribution differs significantly from equilibrium cases.

A novel relation between Casimir force and non-equilibrium heat is proposed.

Abstract

Long-ranged correlations generically exist in non-equilibrium fluid systems. In the case of a non-equilibrium steady state caused by a temperature gradient the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently the Casimir force or pressure due to these fluctuations or correlations have been discussed in great detail. In this paper the notion of a Casimir work is introduced and a novel way to measure the non-equilibrium Casimir force is suggested. In particular, the non-equilibrium Casimir force is related to a non-equilibrium heat and not, as in equilibrium, to a volume derivative of an average energy. The non-equilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The non-equilibrium work distribution is also computed, and contrasted to work distributions in systems with short-range correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in non-equilibrium steady states are not explicit enough to illustrate any of these interesting features.