Probability of second law violations in shearing steady states

Abstract

We propose a new definition of natural invariant measure for trajectory segments of finite duration for a many-particle system. On this basis we give an expression for the probability of fluctuations in the shear stress of a fluid in a nonequilibrium steady state far from equilibrium. In particular we obtain a formula for the ratio that, for a finite time, the shear stress reverse sign, violating the second law of thermodynamics. Computer simulations support this formula.