Journal of Statistical Physics, Vol. 24, No. 2, 1981. p. 325-343.
It is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure. These are chosen by considering the totality of future possibilities for observation on the system. It is shown that this entropy is necessarily a nondecreasing function of the time t. There is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal...