Summary
Within the framework of nonequilibrium statistical mechanics, we systematically study the mathematical structure of the subdynamics proposed by the Brussels school. The solution of the Liouville equation is obtained by the use of an eigenfunction expansion. It is found that the subdynamics projection operator in the form given by the Brussels school is not well defined, and that the irreversibility is not a derived consequence of the theory as it was claimed by them, but it is rather anad hoc assumption.
Riassunto
Nell’ambito della meccanica statistica delle condizioni di non equilibrio, si studia sistematicamente la struttura matematica delle sottodinamiche proposte dalla scuola di Brussels. Si ottiene la soluzione dell’equazione di Liouville per mezzo di uno sviluppo in serie di autofunzioni. Si trova che l’operatore di proiezione delle sottodinamiche, nella forma proposta dalla scuola di Brussels, non è ben definito e che l’irreversibilità non è una conseguenza che discende dalla loro teoria, come essi dicono, ma piuttosto un’ipotesiad hoc.
Резюме
В рамках неравновесной статистической механики мы систематически исследуем математическю субдинамики, предложенной Брюссельской школой. Используя разложение по собственным фучкциям, получается решение уравнения Лиуилля. Получается, что проекционный оператор субдинамики в форме, предложенной Брыссельской школой, не является хорошо очределенным, и что необратимость не является следствием теории, как это утверждалось, а скорее всего является предположением для данного спучая.
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Supported in part by the U.S. Atomic Energy Commission.
Traduzione a cura della Redazione.
Перевебено ребакицей.
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Chiang, C.C. Structure of subdynamics in nonequilibrium statistical mechanics. Nuov Cim B 25, 125–144 (1975). https://doi.org/10.1007/BF02737669
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DOI: https://doi.org/10.1007/BF02737669