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Quantum thermodynamics of nonequilibrium. Onsager reciprocity and dispersion-dissipation relations

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Abstract

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results.

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References

  1. G. P. Beretta, Sc. D. Thesis, M.I.T. (1981), unpublished; G. P. Beretta, E. P. Gyftopoulos, J. L. Park, and G. N. Hatsopoulos,Nuovo Cimento B,82, 169 (1984).

  2. G. P. Beretta, E. P. Gyftopoulos, and J. L. Park,Nuovo Cimento B,87, 77 (1985).

    Google Scholar 

  3. L. Onsager,Phys. Rev. 37, 405 (1931);38, 2265 (1931).

    Google Scholar 

  4. H. B. G. Casimir,Rev. Mod. Phys. 17, 343 (1945).

    Google Scholar 

  5. J. L. Park and R. F. Simmons, Jr., inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York, 1982).

    Google Scholar 

  6. H. B. Callen, Thesis, M.I.T. (1947), unpublished.

  7. R. Kubo,J. Phys. Soc. Jpn. 12, 570 (1957).

    Google Scholar 

  8. S. R. de Groot,Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 1951).

    Google Scholar 

  9. H. B. Callen, M. L. Barasch, and J. L. Jackson,Phys. Rev. 88, 1382 (1952).

    Google Scholar 

  10. L. Onsager and S. Machlup,Phys. Rev. 91, 1505 (1953).

    Google Scholar 

  11. S. R. De Groot,Thermodynamics of Irreversible Processes (Interscience, New York, 1950).

    Google Scholar 

  12. I. Prigogine,Introduction to Thermodynamics of Irreversible Processes (C. C. Thomas, Springfield, Illinois, 1965).

    Google Scholar 

  13. R. D. Levine,J. Chem. Phys. 65, 3302 (1976).

    Google Scholar 

  14. G. N. Hatsopoulos and E. P. Gyftopoulos,Found. Phys. 6, 15, 127, 439, 561 (1976).

    Google Scholar 

  15. G. P. Beretta,Int. J. Theor. Phys. 24, 119, 1249 (1985).

    Google Scholar 

  16. G. P. Beretta, inFrontiers of Nonequilibrium Statistical Physics, G. T. Moore and M. O. Scully, eds. (Plenum, New York, 1985).

    Google Scholar 

  17. H. B. Callen and T. A. Welton,Phys. Rev. 83, 34 (1951); R. F. Greene and H. B. Callen,Phys. Rev. 83, 1231 (1951); H. B. Callen and R. F. Greene,Phys. Rev. 86, 702 (1952); R. F. Greene and H. B. Callen,Phys. Rev. 88, 1387 (1952).

    Google Scholar 

  18. H. Nyquist,Phys. Rev. 32, 110 (1928).

    Google Scholar 

  19. G. P. Beretta,J. Math. Phys. 27, 305 (1985).

    Google Scholar 

  20. W. Band and J. L. Park,Found. Phys. 1, 133 (1970).

    Google Scholar 

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Beretta, G.P. Quantum thermodynamics of nonequilibrium. Onsager reciprocity and dispersion-dissipation relations. Found Phys 17, 365–381 (1987). https://doi.org/10.1007/BF00733374

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  • DOI: https://doi.org/10.1007/BF00733374

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