Abstract
A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It is a central quantity by which various forms of the fluctuation theorem are obtained. The two kinds of the stochastic dynamics are investigated: the Langevin dynamics for an even-parity state and the Brownian motion of a single particle. Mathematical ambiguities in deriving the functional form of the entropy production, which depends on path in state space, are clarified by using a rigorous quantum mechanical approach.
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D. J. Evans, E. G. D. Cohen and G. P. Morriss, Phys. Rev. Lett. 71, 2401 (1993).
C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
G. E. Crooks, J. Stat. Phys. 90, 1481 (1998).
J. Kurchan, J. Phys. A 31, 3719 (1998).
J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 333 (1999).
G. M. Wang, E. M. Sevick, E. Mittag, D. J. Searles and D. J. Evans, Phys. Rev. Lett. 89, 050601 (2002).
E. H. Trepagnier, C. Jarzynski, F. Ritort, G. E. Crooks, C. J. Bustamante and J. Liphardt, Proc. Natl. Acad. Sci. 101, 15038 (2004).
G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. 98, 3658 (2001).
N. Garnier and S. Ciliberto,. Phys. Rev. E 71, 060101 (2005).
F. Douarche, S. Joubaud, N. B. Garnier, A. Petrosyan and S. Ciliberto, Phys. Rev. Lett. 97, 140603 (2006).
S. Joubaud, N. B. Garnier and S. Ciliberto, Europhys. Lett. 82, 30007 (2008).
J. Liphardt, S. Dumont, S. B. Smith, I. Tinico Jr and C. Bustamante, Science 296, 1832 (2002).
D. Collin, F. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco, Jr and C. Bustamante, Nature 437, 231 (2005).
K. Hayashi, H. Ueno, R. Iino and H. Noji, Phys. Rev. Lett. 104, 218103 (2010).
D. Y. Lee, C. Kwon and H. K. Pak, Phys. Rev. Lett. 114, 060603 (2015).
L. Onsager and S. Machlup, Phys. Rev. 91, 1505 (1953)
S. Machlup and L. Onsager, ibid. 91, 1512 (1953).
J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976).
C. E. Shannon, Bell. Sys. Tech. J. 27, 379 (1948).
T. Speck and U. Seifert, J. Phys. A 38, L581 (2005)
U. Seifert, Phys. Rev. Lett. 95, 040602 (2005).
M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha Rev. Mod. Phys. 85, 1143 (2013).
S. Ramaswamy, R. A. Simha, and J. Toner, Europhys. Lett. 62 196 (2003).
F. Schweitzer, Brownian Agents and Active Particles (Springer, Berlin, 2002)
P. Romanczuk, M. Bär, W. Ebeling, B. Lindner and L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012)
C. Ganguly and D. Chaudhuri, Phys. Rev. E 88, 032102 (2013)
D. Chaudhuri, ibid. 90, 022131 (2014).
H. Hirakawa, S. Hiramatsu and Y. Ogawa, Phys. Lett. 63A, 199 (1977)
J.-M. Courty, A. Heidmann and M. Pinard, Eur. Phys. J. D 17, 399 (2001)
G. Jourdan, G. Torricelli, J. Chevrier, and F. Comin, Nanotechnology 18, 475502 (2007).
K. H. Kim and H. Qian, Phys. Rev. Lett. 93, 120602 (2004); Phys. Rev. E 75, 022102 (2007).
C. Kwon, J. Um, J. D. Noh and H. Park (unpublished).
R. E. Spinney and I. J. Ford, Phys. Rev. Lett. 108, 170603 (2012); Phys. Rev. E 85, 051113 (2012); ibid. 86, 021127 (2012).
H. K. Lee, C. Kwon and H. Park, Phys. Rev. Lett 110, 050602 (2013).
C. Kwon, J. Yeo, H. K. Lee and H. Park (unpublished).
H. Risken, The Fokker-Planck Equation: methods of solution and applications, 2nd Edition (Springer-Verlag, Berlin, 1989).
C. Kwon, J. D. Noh and H. Park, Phys. Rev. E 83, 061145 (2011).
J. S. Lee, C. Kwon and H. Park, Phys. Rev. E 87, 020104(R) (2013); J. Stat. Mech. P11002 (2013).
C. Kwon, P. Ao and D. Thouless, Proc. Natl. Acad. Sci. 102, 13029 (2005).
C. Kwon and P. Ao, Phys. Rev. E 84, 061106 (2011).
M. Esposito and C. Van den Broeck, Phys. Rev. Lett. 104, 090601 (2010).
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Kwon, C. Path-dependent entropy production. Journal of the Korean Physical Society 67, 785–791 (2015). https://doi.org/10.3938/jkps.67.785
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DOI: https://doi.org/10.3938/jkps.67.785