(Received April 13, 1960)
The development of a satisfactory statistical mechanics for non-equilibrium states has been retarded by the difficulty of making a satisfactory definition of “local temperature”, that is, a definition which does not depend on the very restrictive assumption of local equilibrium. We first define, for any subvolume ΔV of the system, the “local statistical operator” W(ΔV), which can be deduced directly from the statistical operator (density matrix) U of the system as a whole. Next, we define a local entropy S(ΔV) and a local energy E(ΔV). Finally, we introduce a new requirement for the macroscopic independent variables which define the macroscopic state of the system: such variables must be directly deducible from a knowledge of the present state (density matrix) of the system, without reference to its future time development, i. e., without reference to its Hamiltonian H. Of any pair of thermodynamically conjugate variables, at most one is permissible in the light of this requirement. In particular, volume, particle numbers, and entropy are permissible macroscopic independent variables; pressure, chemical potential, and temperature are not. These latter are permissible as dependent variables, only, unless the system happens to be in equilibrium.
URL : http://ptp.ipap.jp/link?PTP/24/741/
DOI : 10.1143/PTP.24.741