Abstract
We present a simple derivation of the integral fluctuation theorems for excess and housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the integral fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it naturally leads to the integral fluctuation theorem for housekeeping heat. We also derive the modified detailed fluctuation theorems for the excess and housekeeping heats.
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References
L.D. Landau, E.M. Lifshitz, in Statistical Physics, 3rd edn. (Butterworth-Heinemann, 1980), Part 1
U. Seifert, Phys. Rev. Lett. 95, 040602 (2005)
U. Seifert, Eur. Phys. J. B 64, 423 (2008)
U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)
Y. Oono, M. Paniconi, Prog. Theor. Phys. Suppl. 130, 29 (1998)
T. Hatano, S. Sasa, Phys. Rev. Lett. 86, 3463 (2001)
T. Speck, U. Seifert, J. Phys. A 38, L581 (2005)
R. García-García, V. Lecomte, A.B. Kolton, D. Domínguez, J. Stat. Mech. 2012, P02009 (2012)
M. Esposito, C. Van den Broeck, Phys. Rev. Lett. 104, 090601 (2010)
M. Esposito, C. van den Broeck, Phys. Rev. E 82, 011143 (2010)
M. Esposito, C. van den Broeck, Phys. Rev. E 82, 011144 (2010)
R.E. Spinney, I.J. Ford, Phys. Rev. Lett. 108, 170603 (2012)
R.E. Spinney, I.J. Ford, Phys. Rev. E 86, 021127 (2012)
R.E. Spinney, I.J. Ford, Phys. Rev. E 85, 51113 (2012)
H.K. Lee, C. Kwon, H. Park, Phys. Rev. Lett. 110, 050602 (2013)
S. Sasa, J. Stat. Mech. 2014, P01004 (2014)
V.Y. Chernyak, M. Chertkov, C. Jarzynski, J. Stat. Mech. 2006, P08001 (2006)
O. Narayan, A. Dhar, J. Phys. A 37, 63 (2004)
K. Sekimoto, J. Phys. Soc. Jpn 66, 1234 (1997)
K. Sekimoto, Prog. Theor. Phys. Suppl. 130, 17 (1998)
G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)
G.E. Crooks, Phys. Rev. E 61, 2361 (2000)
P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)
P. Talkner, M. Campisi, P. Hänggi, J. Stat. Mech. 2009, P02025 (2009)
J.D. Noh, J. Park, Phys. Rev. Lett. 108, 240603 (2012)
G.E. Crooks, Phys. Rev. E 60, 2721 (1999)
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Lahiri, S., Jayannavar, A. Fluctuation theorems for excess and housekeeping heat for underdamped Langevin systems. Eur. Phys. J. B 87, 195 (2014). https://doi.org/10.1140/epjb/e2014-50379-6
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DOI: https://doi.org/10.1140/epjb/e2014-50379-6