Boltzmann's Entropy and Large Deviation Lyapunov Functionals for Closed   and Open Macroscopic Systems
  I give a brief overview of the resolution of the apparent problem of reconciling time symmetric microscopic dynamic with time asymmetric equations describing the evolution of macroscopic variables. I then show how the large deviation function of the stationary state of the microscopic system can be used as a Lyapunov function for the macroscopic evolution equations. 
Joel L. Lebowitz
math-ph cond-mat.stat-mech math.MP