Notes on Variation Principles in the Quantum and Classical Theories of Transport Processes

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Two notes on the variation principles in the theory of transport processes are presented. The first note is concerned with a revised form of the quantum variation principle which has been proposed previously concerning the Neumann equation for a system externally disturbed. In the variation principle in the new form the density operator for a system with Hamiltonian H appears necessarily coupling with that for the system with the time-reversed Hamiltonian H in contrast with the previous form in which there appear a pair of density operators representing the system exposed to incoming or outgoing external disturbances. A closer analogy between the quantum and classical variation principles is thus found and the reduction from the former to the latter principles is executed more naturally. In the case of no-magnetic field in which H^^- is identical with H, only a single density operator comes into the variational expression. In the presence of magnetic field H the transport problems in the respective cases of magnetic fields H and -H come into the variation principle coupling with each other in the same way as in the classical variation principle. The second note is concerned with the relation between the variation principle in the transport theory based on the Boltzmann equation and that in the thermostatistical theory by Onsager. The former principle is reduced to the latter by assuming a suitable variational distribution function.
一般社団法人日本物理学会の論文
1973-05-25

Notes on Variation Principles in the Quantum and Classical Theories of Transport Processes

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