Fine-grained and coarse-grained entropy in problems of statistical mechanics

We consider dynamical systems with a phase space Γ that preserve a measure μ. A partition of Γ into parts of finite μ-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on Γ and generalizes the usual (ordinary or fine-grained) Gibbs entropy. We study the approximation properties of the coarse-grained entropy under refinement of the partition and also the properties of the coarse-grained entropy as a function of time. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 120–137, April, 2007.