Thermodynamical properties in nonequilibrium statistical mechanics

The derivation of nonequilibrium thermodynamics is discussed from a microscopic point of view. We start from a generalized Fokker-Planck equation which is obtained from the classical Liouville equation by a projection operator method. Then we define thermodynamical quantities, and derive exact relations which must be satisfied by these thermodynamical quantities. The form of these relations suggests that they result in the ordinary thermodynamical relations. Indeed we derive some of the ordinary thermodynamical laws by coarse-graining procedures.