I will present an overview of how the time evolution of macroscopic (or mesoscopic) variables in an isolated system can be understood qualitatively in terms of the Boltzmann entropy. This entropy will always increase, even in systems far from local equilibrium. When these variables satisfy an autonomous evolution equation there will always be an $cal H$-theorem, e.g. the Boltzmann (Enskog) equation for gases and the Peierles’ equation for phonons. Non isolated systems will also be considered.

References:

S. Goldstein and J. L. Lebowitz, On the (Boltzmann) Entropy of Nonequilibrium Systems. Physica D, 2004. Los Alamos cond-mat/0304251 and Texas Archive 03-167.

P.L. Garrido, S. Goldstein and J. L. Lebowitz, The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium. Physical Review Letters, 92, 050602, 2003. Los Alamos cond-mat/0310575.

Rutgers/IHES