Abstract
Recently, there has been a considerable progress on the issue of the thermodynamic second law, which is known as the law of entropy increase or irreversibility. In particular, a novel symmetry known as the Gallavotti-Cohen symmetry is found in nonequilibrium (NEQ) fluctuations, which leads to so-called fluctuation theorems. The thermodynamic second law is a simple corollary of fluctuation theorems, from which one can predict quantitatively how often NEQ processes violate the law of entropy increase. Violations disappear in the thermodynamic limit, but can be observed reasonably well in small systems. In this article, we will briefly introduce the stochastic thermodynamics and derive various fluctuation theorems, including the total entropy production (EP), the work-free-energy relation, the excess and house-keeping EP, and the information entropy.
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References
D. J. Evans, E. G. D. Cohen and G. P. Morriss, Phys. Rev. Lett. 71, 2401 (1993).
G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995).
C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
J. Kurchan, J. Phys. A 31, 3719 (1998).
G. E. Crooks, J. Stat. Phys. 90, 1481 (1998).
J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 333 (1999).
T. Hatano and S. I. Sasa, Phys. Rev. Lett. 86, 3463 (2001).
T. Speck and U. Seifert, J. Phys. A 38, L581 (2005).
T. Sagawa and M. Ueda, Phys. Rev. Lett. 100, 080403 (2008); ibid. 102, 250602 (2009); ibid. 104, 090602 (2010).
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, J. Korean Phys. Soc. 68, 633 (2016).
J. Yeo, C. Kwon, H. K. Lee and H. Park, J. Stat. Mech. 093205 (2016).
J. Liphardt, S. Dumont, S. B. Smith, I. Tinoco 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).
D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud and A. Petrosyan, Phys. Rev. Lett. 98, 150601 (2007).
S. Ciliberto, A. Imparato, A. Naert and M. Tanase, Phys. Rev. Lett. 110, 180601 (2013).
D. Y. Lee, C. Kwon and H. K. Pak, Phys. Rev. Lett. 114, 060603 (2015).
U. Seifert, Phys. Rev. Lett. 116, 020601 (2016).
T. Speck and U. Seifert, J. Stat. Mech. 2007, L09002 (2007).
Y. Utsumi, D. S. Golubev, M. Marthaler, G. Schön and K. Kobayashi, Phys. Rev. B 86, 075420 (2012).
J. Kurchan, arXiv:cond-mat/0007360
H. Tasaki, arXiv:cond-mat/0009244
M. Campisi, P. Talkner and P. Hänggi, Phys Rev. Lett. 102, 210401 (2009)
M. Campisi, P. Hänggi and P. Talkner, Rev. Mod. Phyhs. 83, 771 (2011).
K. Sekimoto, Prog. Theor. Phys. Suppl. 130, 17 (1998).
U. Seifert, Phys. Rev. Lett. 95, 040602 (2005).
M. Esposito and C. Van den Broeck, Phys. Rev. Lett. 104, 090601 (2010).
J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976).
H. Hinrichsen, C. Gogolin and P. Janotta, J. Phys.: Conf. Ser. 297, 012011 (2011).
J. Farago, J. Stat. Phys. 107, 781 (2002); Physica A 331, 69 (2004).
R. van Zon and E. G. D. Cohen, Phys. Rev. Lett. 91, 110601 (2003).
J. D. Noh and J-M. Park, Phys. Rev. Lett. 108, 240603 (2012).
J. S. Lee, C. Kwon and H. Park, Phys. Rev. E 87, 020104(R) (2013); J. Stat. Mech. 2013, P11002 (2013).
K. Kim, C. Kwon and H. Park, Phys. Rev. E 90, 032117 (2014).
H. K. Lee, S. Lahiri and H. Park, Phys Rev. E 96, 022134 (2017).
C. Ganguly and D. Chaudhuri, Phys. Rev. E 88, 032102 (2013)
D. Chaudhuri, Phys. Rev. E 90, 022131 (2014).
H-M. Chun and J. D. Noh, J. Stat. Mech. 2018, 023208 (2018).
K. H. Kim and H. Qian, Phys. Rev. Lett. 93, 120602 (2004); Phys. Rev. E 75, 022102 (2007).
S. Ito and M. Sano, Phys. Rev. E 84, 021123 (2011).
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).
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)
É. Fodor, C. Nardini, M. E. Cates, J. Tailleur, P. Visco and F. van Wijland, Phys. Rev. Lett. 117, 038103 (2016).
S. Ramaswamy, R. A. Simha and J. Toner, Europhys. Lett. 62, 196 (2003).
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).
C. Pérez-Espigares, A. B. Kolton and J. Kurchan, Phys. Rev. E 85, 031135 (2012).
Y. Oono and M. Paniconi, Prog. Theor. Phys. 130, 29 (1998).
In Langevin dynamics, the detailed balance guarantees the parity symmetry, but it does not in Markovian jump dynamics [11–13].
C. Kwon, J. Um and H. Park, EPL 117, 10011 (2017).
J. Um, H. Hinrichsen, C. Kwon and H. Park, New J. Phys. 17, 085001 (2015).
Y. Murashita and M. Esposito, Phys. Rev. E 94, 062148 (2016)
M. Esposito and C. Van den Broeck, Phys. Rev. E 82, 011143 (2010).
J. S. Lee and H. Park (unpublished).
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Park, H. Entropy and Thermodynamic Second Laws: New Perspective - Stochastic Thermodynamics and Fluctuation Theorems. J. Korean Phys. Soc. 72, 1413–1420 (2018). https://doi.org/10.3938/jkps.72.1413
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DOI: https://doi.org/10.3938/jkps.72.1413