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Time‐dependent quantum statistical inequalities
Author(s) -
Golden Sidney
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560070766
Subject(s) - observable , monotonic function , operator (biology) , hamiltonian (control theory) , mathematics , statistical physics , quantum , virial theorem , quantum system , function (biology) , time evolution , initial value problem , physics , quantum mechanics , mathematical analysis , mathematical optimization , biochemistry , chemistry , repressor , evolutionary biology , galaxy , biology , transcription factor , gene
Abstract The following is established. Any system having a temporal evolution which is determined by its Hamiltonian and which has an initial statistical operator that is a completely monotonic function of a given nonnegative and time‐independent observable will evolve in time so that the expectation value of that observable is never less than the initial value. In a suitable time‐averaged sense, for systems having time‐independent Hamiltonians, the velocity and acceleration of the expectation value are shown to be nonnegative. The results obtained depend in no way on the system being macroscopic. A theorem dealing with the energy of a system and another dealing with the virial of a system are derived to illustrate the use of the time‐dependent inequalities.