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Thermodynamic variational relation
Phys. Rev. E 108, 044103 – Published 2 October, 2023
DOI: https://doi.org/10.1103/PhysRevE.108.044103
Abstract
In systems far from equilibrium, the statistics of observables are connected to entropy production, leading to the thermodynamic uncertainty relation (TUR). However, the derivation of TURs often involves constraining the parity of observables, such as considering asymmetric currents, making it unsuitable for the general case. We propose a thermodynamic variational relation (TVR) between the statistics of general observables and entropy production, based on the variational representation of divergences. From this result, we derive a universal TUR and other relations for higher-order statistics of observables.
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References (38)
- G. T. Landi and M. Paternostro, Rev. Mod. Phys. 93, 035008 (2021).
- M. Campisi, P. Hänggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011).
- U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).
- M. Esposito, U. Harbola, and S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009).
- S. Ciliberto, A. Imparato, A. Naert, and M. Tanase, Phys. Rev. Lett. 110, 180601 (2013).
- G. E. Crooks, J. Stat. Phys. 90, 1481 (1998).
- G. E. Crooks, Phys. Rev. E 60, 2721 (1999).
- G. Gallavotti and E. G. D. Cohen, J. Stat. Phys. 80, 931 (1995).
- D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Phys. Rev. Lett. 71, 2401 (1993).
- P. Hänggi and P. Talkner, Nat. Phys. 11, 108 (2015).
- T. B. Batalhão, A. M. Souza, L. Mazzola, R. Auccaise, R. S. Sarthour, I. S. Oliveira, J. Goold, G. De Chiara, M. Paternostro, and R. M. Serra, Phys. Rev. Lett. 113, 140601 (2014).
- S. Pal, T. S. Mahesh, and B. K. Agarwalla, Phys. Rev. A 100, 042119 (2019).
- T. Van Vu and K. Saito, Phys. Rev. X 13, 011013 (2023).
- D. J. Evans and D. J. Searles, Adv. Phys. 51, 1529 (2002).
- C. Jarzynskia, Eur. Phys. J. B 64, 331 (2008).
- C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
- K. Proesmans and J. M. Horowitz, J. Stat. Mech.: Theory Exp. (2019) 054005.
- R. E. Spinney and I. J. Ford, Phys. Rev. E 85, 051113 (2012).
- C. Van den Broeck and R. Toral, Phys. Rev. E 92, 012127 (2015).
- J. M. Horowitz and M. Esposito, Phys. Rev. E 94, 020102(R) (2016).
- C. Jarzynski and D. K. Wójcik, Phys. Rev. Lett. 92, 230602 (2004).
- Y. Hasegawa, Phys. Rev. Lett. 125, 050601 (2020).
- S. Deffner, J. P. Paz, and W. H. Zurek, Phys. Rev. E 94, 010103(R) (2016).
- K. Micadei, G. T. Landi, and E. Lutz, Phys. Rev. Lett. 124, 090602 (2020).
- A. C. Barato and U. Seifert, Phys. Rev. Lett. 114, 158101 (2015).
- T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Phys. Rev. Lett. 116, 120601 (2016).
- M. Polettini, A. Lazarescu, and M. Esposito, Phys. Rev. E 94, 052104 (2016).
- P. Pietzonka and U. Seifert, Phys. Rev. Lett. 120, 190602 (2018).
- Y. Hasegawa and T. Van Vu, Phys. Rev. Lett. 123, 110602 (2019).
- A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Phys. Rev. Lett. 123, 090604 (2019).
- J. M. Horowitz and T. R. Gingrich, Nat. Phys. 16, 15 (2020).
- P. P. Potts and P. Samuelsson, Phys. Rev. E 100, 052137 (2019).
- K. Liu, Z. Gong, and M. Ueda, Phys. Rev. Lett. 125, 140602 (2020).
- D. S. P. Salazar, Phys. Rev. E 106, L062104 (2022).
- A. Dechant and S. Sasa, Proc. Natl. Acad. Sci. USA 117, 6430 (2020).
- L. Ziyin and M. Ueda, Phys. Rev. Res. 5, 013039 (2023).
- Y. Polyanskiy and W. Yihong, Information Theory: From Coding to Learning (Cambridge University Press, Cambridge, UK, 2022).
- D. S. P. Salazar, Phys. Rev. E 107, L062103 (2023).
