Time-reversal symmetry relation for nonequilibrium flows ruled by the   fluctuating Boltzmann equation
  A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random numbers of particles in cells of given position and velocity in the single-particle phase space. The symmetry relation concerns the fluctuating particle and energy currents of the gas flowing between reservoirs or thermalizing surfaces at given particle densities or temperatures. 
Pierre Gaspard
cond-mat.stat-mech