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Il Nuovo Cimento B (1971-1996)

, Volume 87, Issue 1, pp 77–97 | Cite as

Quantum thermodynamics. A new equation of motion for a general quantum system

  • G. P. Beretta
  • E. P. Gyftopoulos
  • J. L. Park
Article

Summary

A novel nonlinear equation of motion is proposed for a general quantum system consisting of more than one distinguishable elementary constituent of matter. In the domain of idempotent quantummechanical state operators, it is satisfied by all unitary evolutions generated by the Schrödinger equation. But, in the broader domain of nonidempotent state operators not contemplated by conventional quantum mechanics, it generates a generally nonunitary evolution, it keeps the energy invariant and causes the entropy to increase with time until the system reaches a state of equilibrium or a limit cycle.

PACS. 03.65. Quantum theory quantum mechanics 

Квантовая термодинамика. Новое уравнение движения для общей квантовой системы

Резюме

Предлагается новое нелинейное уравнение движения для общей квантовой системе, состоящей из более чем одной элементарной составляющей вещества. В области идемпотентных квантовомеханических операторов состояний удовлетворяются все унитарные эволюции, генерированные уравнением Шредингера. В более широкой области неидемпотентных операторов состояний, не рассматриваемой в обычной квантовой механике, возникает неунитарная эволюция, при этом энергия является инвариантной, а энтропия увеличивается со временем, пока система достигает состояния равновесия или предельного цикла.

Riassunto

Si propone una nuova equazione non lineare di evoluzione per un sistema quantistico generale costituito da piú costituenti materiali elementari distinguibili. Nel dominio degli operatori di stato idempotenti della meccanica quantistica, l'equazione è soddisfatta da tutte le evoluzioni unitarie generate dall'equazione di Schrödinger. Ma, nel dominio piú ampio degli operatori di stato non idempotenti, non contemplati dalla meccanica quantistica convenzionale, l'equazione genera un'evoluzione generalmente non unitaria, mantiene costante il valor medio dell'energia e causa aumenti di entropia finchè il sistema non raggiunge uno stato di equilibrio oppure un ciclo limite.

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Copyright information

© Società Italiana di Fisica 1985

Authors and Affiliations

  • G. P. Beretta
    • 1
  • E. P. Gyftopoulos
    • 1
  • J. L. Park
    • 2
  1. 1.Massachusetts Institute of TechnologyCambridge
  2. 2.Washington State UniversityPullman

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