Local properties in non-equilibrium systems

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The development of a satisfactory statisticai mechanics for nonequilibrium states was 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. For any subvolume DELTA V of the system, the "local statistical operator" W( DELTA V), which can be deduced directly from the statistical operator (density matrix) U of the system as a whole, is defined. Local ertropy S( DELTA V) and a local energy E( DELTA V) are also defined. A new requirement for the macroscopic independent variables which define the macroscopic state of the system was introduced: 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 happene to be in equilibrium. (auth)

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