Carnot’s cycle for small systems: Irreversibility and cost of operations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 6, 2000, Pages 7759-7768

  Sekimoto, Ken ^a   Takagi, Fumiko ^b   Hondou, Tsuyoshi ^c  

^a KYOTO UNIVERSITY   (Japan)

^b IBARAKI UNIVERSITY   (Japan)

^c TOHOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COSTS; FREE ENERGY; MASS TRANSFER; MATHEMATICAL MODELS; MAXWELL EQUATIONS; RANDOM PROCESSES; THERMODYNAMIC STABILITY;

LANGEVIN EQUATIONS;

CARNOT CYCLE;

EID: 0034513136     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.7759     Document Type: Article

References (27)

1. See, for example, E. Fermi, Thermodynamics (Dover, New York, 1956).
2. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Pergamon Press, New York, 1980).
3. K. Sekimoto, J. Phys. Soc. Jpn. 66, 1234 (1997).
4. K. Sekimoto and S. Sasa, J. Phys. Soc. Jpn. 66, 3326 (1997).
5. K. Sekimoto, Prog. Theor. Phys. Suppl. 130, 17 (1998).
6. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1966), Vol. I, Chap. 46.
7. J. M. R. Parrondo and P. Espanol, Am. J. Phys. 64, 1125 (1996).
8. Hereafter, multiplication of a fluctuating quantity by another quantity, either fluctuating or nonfluctuating, such as (Formula presented) should be understood in the sense of Stratonovich calculus. See, for example, C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
9. We have noticed that the relation (8) holds without averaging over the ensemble thanks to discussion with Chris Jarzynski. Until now, only its weak form (12) had been shown (see Ref. 4).
10. H. A. Kramers, Physica (Amsterdam) 7, 284 (1940).
11. L. D. Landau and E. M. Lifshitz, Mechanics, 3rd ed. (Pergamon Press, New York, 1976), Sec. 49. (The description in the other editions is less detailed.)
12. K. Sato, K. Sekimoto, T. Hondou, and F. Takagi (unpublished).
13. The general mathematical proof of the adiabatic theorem can be found in T. Kasuga, Proc. Jpn. Acad. 37, 366 (1961)
14. Proc. Jpn. Acad.T. Kasuga37, 372 (1961)
15. Proc. Jpn. Acad.T. Kasuga37, 377 (1961).
16. Katsuhiko Sato (private communication).
17. T. Komatsu and S. Sasa (unpublished).
18. S. Sasa and T. Komatsu, Prog. Theor. Phys. 103, 1 (2000).
19. J. R. Cray, D. F. Escande, and J. L. Tennyson, Phys. Rev. A 34, 4256 (1986).
20. M. O. Magnasco and G. Stolovitzky, J. Stat. Phys. 93, 615 (1998).
21. M. Büttiker, Z. Phys. B: Condens. Matter 68, 161 (1987).
22. M. Matsuo and S. Sasa, Physica A 276, 188 (2000).
23. T. Hondou and K. Sekimoto, Phys. Rev. E (to be published).
24. H. Sakaguchi, J. Phys. Soc. Jpn. 67, 709 (1998).
25. I. Der’enyi and R. D. Astumian, Phys. Rev. E 59, R6219 (1999).
26. See, for example, B. Alberts, D. Bray, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Essential Cell Biology (Garland, New York, 1997), Secs. 5, 12, and 16.
27. R. D. Vale and F. Oosawa, Adv. Biophys. 26, 97 (1990).