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Quantum thermodynamics. A new equation of motion for a single constituent of matter

Квантовая термодинамика. Новое уравнение движения для однокомпонентного вещества

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

A novel nonlinear equation of motion is proposed for quantum systems consisting of a single elementary constituent of matter. It is satisfied by pure states and by a special class of mixed states evolving unitarily. But, in general, it generates a nonunitary evolution of the state operator. 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.

Riassunto

Si propone una nuova equazione di evoluzione per sistemi quantistici composti da un singolo costituente materiale elementare. L'equazione è soddisfatta dall'evoluzione unitaria degli stati puri e di una sottoclasse di stati misti. Ma, in generale, essa genera un'evoluzione non unitaria dell'operatore di stato. L'equazione mantiene costante il valor medio dell'energia e causa aumenti di entropia finché il sistema non raggiunge uno stato di equilibrio oppure un ciclo limite.

Резюме

Для квантовых систем, состоящих из вещества, представляюего одну элементарную компоненту, предлагается новое нелинейное уравнение движения. Уравнение удовлетворяется для чистых состояний и для специального класса смешанных состояний. В общем случае, это уравнение генерирует неунитарную эволюцию оператора состояния. Это уравнение сохраняет энергию инвариантной, вызывает увелиыение энтропии со временем, пока система не достигнет состояния равновесия.

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  16. A referee suggested two other aspects of our theory that need further investigation and clarification. The first is to study the invariance properties of the new equation of motion under the usual symmetry groups. The second is to explore the implications of the nonlinear equation on the quantum theory of measurement.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, 02139, Cambridge, MA

    G. P. Beretta & E. P. Gyftopoulos

  2. Washington State University, 99164, Pullman, WA

    J. L. Park

  3. Thermo Electron Corporation, 02254, Waltham, MA

    G. N. Hatsopoulos

Authors
  1. G. P. Beretta
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  2. E. P. Gyftopoulos
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  3. J. L. Park
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  4. G. N. Hatsopoulos
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Additional information

This work is based on part of a doctoral dissertation submitted by the first author to the Massachusetts Institute of Technology.

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Beretta, G.P., Gyftopoulos, E.P., Park, J.L. et al. Quantum thermodynamics. A new equation of motion for a single constituent of matter. Nuovo Cim B 82, 169–191 (1984). https://doi.org/10.1007/BF02732871

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  • DOI: https://doi.org/10.1007/BF02732871

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