Entropy of classical histories

We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and we prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.