Explanation of the Gibbs paradox within the framework of quantum thermodynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 6, 2006, Pages

  Allahverdyan, A E ^a   Nieuwenhuizen, Th M ^b  

^a YEREVAN PHYSICS INSTITUTE   (Armenia)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; GIBBS FREE ENERGY; MIXING; QUANTUM THEORY;

GIBBS PARADOX; MACROSCOPIC THERMODYNAMICS; MIXING ERGOTROPY; QUANTUM MIXING ENTROPY;

THERMODYNAMICS;

EID: 33745136152     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.066119     Document Type: Article

References (78)

1. L. D. Landau and E. M. Lifshitz, Statistical Physics, I (Pergamon Press, Oxford, 1978).
2. R. Balian, From Microphysics to Macrophysics (Springer, Berlin, 1992), Vol. I.
3. J. Willard Gibbs, On the Equilibrium of Heterogeneous Substances (Connecticut Academy of Science, 1875-1878) pp. 108-248;
4. J. Willard Gibbs, The Scientific Papers, (Longman, Green and Co., New York, 1906), pp. 165-168.
5. Selected Papers on Thermodynamics and Statistical Physics (Cambridge University Press, London, 1951).
6. E. Schrödinger, Statistical Thermodynamics (Cambridge University Press, London, 1952).
7. I. E. Tamm, Usp. Fiz. Nauk UFNAAG 0042-1294 6, 112 (1926).
8. A. Landé, New Foundations of Quantum Mechanics (Cambridge University Press, Cambridge, England, 1965);
9. Foundations of Quantum Theory (Yale University Press, Yale, 1955).
10. M. J. Klein, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1996106 26, 80 (1958).
11. V. L. Luboshitz and M. I. Podgoretskii, Sov. Phys. Usp. SOPUAP 0038-5670 14, 662 (1972).
12. Ya. M. Gelfer, V. L. Luboshitz, and M. I. Podgoretskii, Gibbs Paradox and Identity of Particles in Quantum Mechanics (Nauka, Moscow, 1975) (in Russian).
13. A. M. Lesk, J. Phys. A JPHAC5 0305-4470 13, L111 (1980).
14. Yu. S. Varshavskii and A. B. Sheinin, Dokl. Akad. Nauk SSSR DANKAS 0002-3264 148, 1099 (1963).
15. N. G. van Kampen, in Essays in Theoretical Physics in Honor of Dirk ter Haar, edited by, W. E. Parry, (Pergamon, Oxford, 1984).
16. C. Y. Tseng and A. Caticha, e-print cond-mat/0109324.
17. D. Dieks and V. van Dijk, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.15571 56, 430 (1988).
18. L. A. Blumenfeld and A. Yu. Grosberg, Biophysics (Engl. Transl.) BIOPAE 0006-3509 40, 653 (1995).
19. Shu-Kun Lin, Electron. J. Theor. Chem. EJTCFB 1082-4928 1, 135 (1996).
20. E. T. Jaynes, in Maximum Entropy and Bayesian Methods, edited by, C. R. Smith, G. J. Erickson, and, P. O. Neudorfer, (Kluwer, Dordrecht, 1992).
21. A. E. Allahverdyan, R. Balian, and Th. M. Nieuwenhuizen, J. Mod. Opt. JMOPEW 0950-0340 51, 2703 (2004).
22. A. E. Allahverdyan, and Th. M. Nieuwenhuizen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056117 64, 056117 (2001).
23. P. A. Corning and S. J. Kline, Syst. Res. Behav. Sci. SRBSF9 1092-7026 15, 273 (1998).
24. E. Schrödinger, What is Life? (Cambridge University Press, Cambridge, England, 1944).
25. M. O. Scully, Y. Rostovtsev, Z. Sariyanni, and M. S. Zubairy, Physica E (Amsterdam) PELNFM 1386-9477 29, 29 (2005);
26. Y. Rostovtsev, Z. Sariyanni, M. S. Zubairy, and M. O. Scully, IEEE Trans. Adv. Packag. ITAPFZ 1521-3323 29, 40 (2005);
27. Z. Sariyanni, Y. Rostovtsev, M. S. Zubairy, and M. O. Scully, IEEE Trans. Adv. Packag. ITAPFZ 1521-3323 29, 47 (2005).
28. R. Rosen, Philos. Sci. PHSCA6 0031-8248 31, 232 (1964).
29. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1995).
30. A. E. Allahverdyan, R. Balian, and Th. M. Nieuwenhuizen, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00150-y 61, 452 (2003);
31. e-print cond-mat/0408316.
32. E. Schrödinger, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 32, 446 (1936);
33. L. P. Hughston, R. Jozsa, and W. K. Wootters, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93)90880-9 183, 14 (1993).
34. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.066102 71, 066102 (2005).
35. G. N. Bochkov and Yu. E. Kuzovlev, Sov. Phys. JETP SPHJAR 0038-5646 45, 125 (1977);
36. I. M. Bassett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.18.2356 18, 2356 (1978);
37. W. Pusz and S. L. Woronowicz, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01614224 58, 273 (1978);
38. A. Lenard, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01011769 19, 575 (1978);
39. W. Thirring, A Course in Mathematical Physics 4: Quantum Mechanics of Large Systems (Springer, Vienna, 1983);
40. H. Tasaki, e-print cond-mat/0009244;
41. J. Kurchan, e-print cond-mat/0007360;
42. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Physica A PHYADX 0378-4371 10.1016/S0378-4371(01)00605-7 305, 542 (2002).
43. G. Lindblad, Non-Equilibrium Entropy and Irreversibility (Reidel, Dordrecht, 1983).
44. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.046107 71, 046107 (2005).
45. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.1799 85, 1799 (2000);
46. Th. M. Nieuwenhuizen and A. E. Allahverdyan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.036102 66, 036102 (2002).
47. D. Janzing, J. Stat. Phys. (to be published), e-print quant-ph/0502019.
48. P. Perrot, A to Z of Thermodynamics (Oxford University Press, New York, 1998).
49. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-10222-0 66, 419 (2004);
50. e-print cond-mat/0401574.
51. V. Jurdjevic and H. J. Sussmann, J. Differ. Equations JDEQAK 0022-0396 10.1016/0022-0396(72)90035-6 12, 313 (1972);
52. A. G. Butkovskiy and Yu. I. Samoilenko, Control of Quantum Mechanical Processes and Systems (Kluwer Academic, Dordrecht, 1990).
53. D. Janzing, e-print quant-ph/0511271.
54. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and its Applications (Academic Press, New York, 1979).
55. S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.3439 72, 3439 (1994);
56. C. A. Fuchs and C. M. Caves, Open Syst. Inf. Dyn. OSIDFU 1230-1612 3, 1 (1995);
57. e-print quant-ph/9604001.
58. D. J. C. Bures, Trans. Am. Math. Soc. TAMTAM 0002-9947 135, 199 (1969);
59. A. Uhlmann, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(76)90060- 4 9, 273 (1976);
60. M. Hübner, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92) 91004-B 163, 239 (1992);
61. R. Jozsa, J. Mod. Opt. JMOPEW 0950-0340 41, 2315 (1994).
62. M. O. Scully, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87. 220601 87, 220601 (2001);
63. M. O. Scully, 0031-9007 Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.050602 88, 050602 (2002);
64. Y. V. Rostovtsev, A. B. Matsko, N. Nayak, M. S. Zubairy, and M. O. Scully, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.053811 67, 053811 (2003);
65. A. E. Hill, Yu. V. Rostovtsev, and M. O. Scully, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.043802 72, 043802 (2005).
66. T. Feldmann and R. Kosloff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.4774 61, 4774 (2000);
67. R. Kosloff and T. Feldmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.055102 65, 055102 (R) (2002);
68. Y. Rezek and R. Kosloff, e-print quant-ph/0601006;
69. J. P. Palao, R. Kosloff, and J. M. Gordon, e-print quant-ph/0106048.
70. J. Gemmer, A. Otte, and G. Mahler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1927 86, 1927 (2001);
71. J. Gemmer and G. Mahler, Eur. Phys. J. D EPJDF6 1434-6060 10.1007/s100530170012 17, 385 (2001);
72. J. Gemmer and G. Mahler, Eur. Phys. J. D EPJDF6 1434-6060 31, 249 (2003).
73. J. Gemmer, M. Michel, and G. Mahler, Quantum Thermodynamics, Vol. 657 of Lecture Notes in Physics (Springer, Berlin, 2004).
74. A. E. Allahverdyan, R. Serral Gracia, and Th. M. Nieuwenhuizen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.260404 93, 260404 (2004);
75. A. E. Allahverdyan, R. Serral Gracia, and Th. M. Nieuwenhuizen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.046106 71, 046106 (2005).
76. D. Janzing, P. Wocjan, R. Zeier, R. Geiss, and Th. Beth, Int. J. Theor. Phys. IJTPBM 0020-7748 39, 2217 (2000).
77. Th. M. Nieuwenhuizen and A. E. Allahverdyan, in Quantum Limits to the Second Law, edited by, D. P. Sheenan, AIP Conf. Proc. APCPCS 0094-243X (AIP, Melville, NY, 2002), p. 436.
78. R. C. Tolman, The Principles of Statistical Mechanics (Oxford University Press, London, 1938).