On the validity of entropy production principles for linear electrical circuits

Journal of Statistical Physics

Volumn 129, Issue 4, 2007, Pages 725-740

  Bruers, Stijn ^a   Maes, Christian ^a   Netočný, Karel ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b INSTITUTE OF PHYSICS   (Czech Republic)

Author keywords

Entropy production; Nonequilibrium fluctuations; Variational principles

Indexed keywords

EID: 35348978670     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9412-z     Document Type: Article

References (28)

1. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Minimum dissipation principle in stationary non equilibrium states. J. Stat. Phys. 116, 831 (2004)
2. Bruers, S.: Classification and discussion of macroscopic entropy production principles. arXiv:cond-mat/0604482
3. Crooks, G.E.: Path-ensemble averages in systems driven far from equilibrium. Phys. Rev. E 61, 2361-2366 (2000)
4. Dembo, A., Zeitouni, O.: Large Deviation Techniques and Applications. Jones and Barlett, Boston (1993)
5. Derrida, B.: Non equilibrium steady states: fluctuations and large deviations of the density and of the current. arXiv:cond-mat/0703762v1
6. Donsker, M.D., Varadhan, S.R.: Asymptotic evaluation of certain Markov process expectations for large time, I. Commun. Pure Appl. Math. 28, 1 (1975)
7. Dürr, D., Bach, A.: The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process. Commun. Math. Phys. 60, 153-170 (1978)
8. Graham, R.: Path integral formulation of general diffusion processes. Z. Phys. B 26, 281-290 (1977)
9. de Groot, S.R., Mazur, P.: Non-equilibrium Thermodynamics. North-Holland, Amsterdam (1969)
10. Hjelmfelt, A., Ross, J.: Thermodynamic and stochastic theory of electrical circuits. Phys. Rev. A 45, 2201 (1992)
11. Jaynes, E.T.: The minimum entropy production principle. Ann. Rev. Phys. Chem. 31, 579-601 (1980)
12. Jiang, D.-Q., Qian, M., Qian, M.-P.: Mathematical Theory of Nonequilibrium Steady States. Lecture Notes in Mathematics, vol. 833. Springer, New York (2004)
13. Jordan, A.N., Suhorukov, E.V., Pilgram, S.: Fluctuation statistics in networks: a stochastic path integral approach. J. Math. Phys. 45, 4386 (2004)
14. Landauer, R.: Inadequacy of entropy and entropy derivatives in characterizing the steady state. Phys. Rev. A 12, 636-638 (1975)
15. Landauer, R.: Stability and entropy production in electrical circuits. J. Stat. Phys. 13, 1-16 (1975)
16. Landauer, R.: Statistical physics of machinery: forgotten middle-ground. Physica A 194, 551-562 (1993)
17. Maes, C.: Fluctuation theorem as a Gibbs property. J. Stat. Phys. 95, 367-392 (1999)
18. Maes, C.: On the origin and the use of fluctuation relations for the entropy. In: Dalibard, J., Duplantier, B., Rivasseau, V. (eds.) Séminaire Poincaré, vol. 2, pp. 29-62. Birkhäuser, Basel (2003)
19. Maes, C., Netočný, K.: Time-reversal and entropy. J. Stat. Phys. 110, 269-310 (2003)
20. Maes, C., Netočný, K.: Static and dynamical nonequilibrium fluctuations. C. R. Phys. 8, 591-597 (2007)
21. Maes, C., Netočný, K.: Minimum entropy production principle from a dynamical fluctuation law. J. Math. Phys. 48, 053306 (2007)
22. Maes, C., Netočný, K.: The canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states. arXiv:cond-mat/0705. 2344
23. Martyushev, L.M., Nazarova, A.S., D Seleznev, V.: On the problem of the minimum entropy production in the nonequilibrium stationary state. J. Phys. A: Math. Theory 40, 371-380 (2007)
24. Onsager, L., Machlup, S.: Fluctuations and irreversible processes. Phys. Rev. 91, 1505-1512 (1951)
25. Prigogine, I.: Introduction to Non-Equilibrium Thermodynamics. Wiley, New York (1962)
26. Varadhan, S.R.S.: Large Deviations and Entropy. In: Greven, A., Keller, G., Warnecke, G. (eds.) Entropy. Princeton University Press, Princeton and Oxford (2003)
27. Ziegler, H.: An Introduction to Thermomechanics. North-Holland, Amsterdam (1983)
28. Županović, P., Juretić, D., Botrić, S.: Kirchhoff's loop law and the maximum entropy production principle. Phys. Rev. E 70, 056108 (2004)