Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Beretta, Gian Paolo (2006)
Languages: English
Types: Preprint
Subjects: Quantum Physics
We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy states it reduces to standard unitary QM. The nonlinear dynamical group of QT is construed so that the second law emerges as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituents. It implements two fundamental ansatzs. The first is that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated system admits also states that must be described by non-idempotent density operators (nonzero entropy). The second is that for such additional states the law of causal evolution is determined by the simultaneous action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituents, and (in forward time) drives any density operator, no matter how far from TE, in the 'direction' of steepest entropy ascent (maximal entropy increase). The equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also backwards in time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] V. Gorini and E.C.G. Sudarshan, in Foundations of Quantum Mechanics and Ordered Linear Spaces (Advanced Study Institute, Marburg, 1973), Editors A. Hartk¨amper and H. Neumann, Lecture Notes in Physics, vol. 29, p.260-268.
    • [2] V. Gorini, A. Kossakowski and E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976).
    • [3] G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
    • [4] E.B. Davies, Rep. Math. Phys. 11, 169 (1977).
    • [5] H. Spohn and J. Lebowitz, Adv. Chem. Phys. 38, 109 (1978).
    • [6] R. Alicki, J. Phys. A 12, L103 (1979).
    • [7] B. Misra, I. Prigogine, and M. Courbage , Proc. Natl. Acad. Sci. USA, 76, 3607, 4768 (1979).
    • [8] M. Courbage and I. Prigogine, Proc. Natl. Acad. Sci. USA, 80, 2412 (1983).
    • [9] G.P. Beretta, in Frontiers of Nonequilibrium Statistical Physics, proceedings of the NATO Advanced Study Institute, Santa Fe, June 1984, Editors G.T. Moore and M.O. Scully (NATO ASI Series B: Physics 135, Plenum Press, New York, 1986), p. 193 and p. 205.
    • [10] G.P. Beretta, in The Physics of Phase Space, edited by Y.S. Kim and W.W. Zachary (Lecture Notes in Physics 278, Springer-Verlag, New York, 1986), p. 441.
    • [11] H. Margenau, The Nature of Physical Reality, McGraw-Hill, 1950.
    • [12] J.L. Park, Am. J. Phys. 36, 211 (1968).
    • [13] J. von Neumann, Mathematical Foundations of Quantum Mechanics, Engl. transl. of the 1931 German edition by R.T. Beyer, Princeton University Press, 1955, pp. 295-346.
    • [14] D. Bohm and J. Bub, Rev. Mod. Phys. 38, 453 (1966).
    • [15] J.L. Park, Philosophy of Science, 35 205, 389 (1968).
    • [16] W. Band and J.L. Park, Found. Phys. 1, 133 (1970).
    • [17] B. d'Espagnat, Conceptual Foundations of Quantum Mechanics, AddisonWesley, second edition, 1976.
    • [18] C.G. Timpson and H.R. Brown, Int. J. Quantum Inf. 3, 679 (2005).
    • [19] G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys. 6, 15, 127, 439, 561 (1976).
    • [20] G.P. Beretta, Int. J. Theor. Phys. 24, 119 (1985).
    • [21] E.P. Gyftopoulos and G.P. Beretta, Thermodynamics: Foundations and Applications, Dover Publications, Mineola, NY, 2005.
    • [22] E.P. Gyftopoulos and E. C¸ ubukc¸u, Phys. Rev. E 55, 3851 (1997).
    • [23] G.P. Beretta, J. Math. Phys. 27, 305 (1986).
    • [24] The stable-equilibrium formulation of the second law of thermodynamics is well known and must be traced to G. N. Hatsopoulos and J. H. Keenan, Principles of General Thermodynamics, Wiley, New York, 1965. It has been further clarified in J. H. Keenan, G. N. Hatsopoulos, and E. P. Gyftopoulos, Principles of Thermodynamics, in Encyclopaedia Britannica, Chicago, 1972, and fully developed in Ref. [21].
    • [25] E. C¸ubukc¸u, Sc.D. thesis, M.I.T., 1993, unpublished.
    • [26] W. Franzen, Phys. Rev. 115, 850 (1959).
    • [27] S.G. Kukolich, Am. J. Phys. 36, 420 (1967).
    • [28] G.P. Beretta, Sc.D. thesis, M.I.T., 1981, unpublished, e-print quant-ph/0509116.
    • [29] G.P. Beretta, e-print quant-ph/0112046.
    • [30] S. Gheorghiu-Svirschevski, Phys. Rev. A 63, 022105, 054102 (2001).
    • [31] G.P. Beretta, Mod. Phys. Lett. A 21, 2799 (2006).
    • [32] E. Schroedinger, Proc. Cambridge Phil. Soc. 32, 446 (1936).
    • [33] G.P. Beretta, Mod. Phys. Lett. A 20, 977 (2005).
    • [34] G.P. Beretta, Phys. Rev. E 73, 026113 (2006).
    • [35] See, e.g., R.C. Dewar, J. Phys. A 38, L371 (2005); P. Z˘upanovi´c, D. Jureti´c, and S. Botri´c, Phys. Rev. E 70 056108 (2004); H. Ozawa, A. Ohmura, R.D. Lorentz, amd T. Pujol, Rev. Geophys. 41, 1018 (2003); H. Struchtrup and W. Weiss, Phys. Rev. Lett. 80, 5048 (1998); and Ref. [30].
    • [36] G.P. Beretta, Found. Phys. 17, 365 (1987).
    • [37] G.P. Beretta, E.P. Gyftopoulos, J.L. Park, and G.N. Hatsopoulos, Nuovo Cimento B 82, 169 (1984); G.P. Beretta, E.P. Gyftopoulos, and J.L. Park, Nuovo Cimento B 87, 77 (1985).
    • [38] J. Maddox, Nature 316, 11 (1985).
    • [39] References [9, 10, 12, 20, 23, 25, 28, 36, 37, 38] are available online at www.quantumthermodynamics.org.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article

Collected from