- Access by Xinjiang University
Relations between heat exchange and Rényi divergences
Phys. Rev. E 97, 042107 – Published 6 April, 2018
DOI: https://doi.org/10.1103/PhysRevE.97.042107
Abstract
In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the Rényi divergences between the initial thermodynamic equilibrium state and the final nonequilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final nonequilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final nonequilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.
Physics Subject Headings (PhySH)
Article Text
References (36)
- C. J. Adkins, Equilibrium Thermodynamics (Cambridge University, New York, 1983).
- C. Jarzynski, Nonequilibrium Equality for Free Energy Difference, Phys. Rev. Lett. 78, 2690 (1997).
- G. Hummer and A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Natl. Acad. Sci. USA 98, 3658 (2001).
- J. Liphardt, S. Dumont, S. B. Smith, I. J. Tinoco, and C. Bustamante, Equilibrium information from nonequilibrium measurements in an experimental test of the Jarzynski equality, Science 296, 1832 (2002).
- D. Collin, F. Ritort, C. Jarzynski, S. Smith, I. Tinoco, and C. Bustamante, Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies, Nature (London) 437, 231 (2005).
- F. Douarche, S. Ciliberto, A. Petrosyan, and I. Rabbiosi, An experimental test of the Jarzynski equality in a mechanical experiment, Europhys. Lett. 70, 593 (2005).
- C. Bustamante, J. Liphardt, and F. Ritort, The nonequilibrium thermodynamics of small systems, Phys. Today 58(7), 43 (2005).
- V. Blickle, T. Speck, L. Helden, U. Seifert, and C. Bechinger, Thermodynamics of a Colloidal Particle in a Time-dependent Nonharmonic Potential, Phys. Rev. Lett. 96, 070603 (2006).
- N. C. Harris, Y. Song, and C. H. Kiang, Experimental Free Energy Surface Reconstruction from Single-Molecule Force Spectroscopy Using Jarzynski's Equality, Phys. Rev. Lett. 99, 068101 (2007).
- J. Kurchan, A quantum fluctuation theorem, arXiv:cond-mat/0007360.
- H. Tasaki, Jarzynski relations for quantum systems and some applications, arXiv:cond-mat/0009244.
- S. Mukamel, Quantum Extension of the Jarzynski Equality: Analogy with Stochastic Dephasing, Phys. Rev. Lett. 90, 170604 (2003).
- P. Talkner, E. Lutz, and P. Hänggi, Work is not an observable, Phys. Rev. E 75, 050102 (2007).
- S. M. An et al. Experimental test of the quantum Jarzynski equality with a trapped-ion system, Nat. Phys. 11, 193 (2015).
- M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009).
- C. Jarzynski, Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, Annu. Rev. Condens. Matter Phys. 2, 329 (2011).
- M. Campisi, P. Hanggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011).
- B. B. Wei and M. B. Plenio, Relations between dissipated work in nonequilibrium process and the family of Rényi divergences, New J. Phys. 19, 023002 (2017).
- B. B. Wei, Links between dissipation and Renyi divergences in the -symmetric quantum mechanics, Phys. Rev. A 97, 012105 (2018).
- B. B. Wei, Dissipation in the Generalized Gibbs Ensemble, arXiv:1711.03855.
- X. Y. Guo et al. Demonstration of irreversibility and dissipation relation of thermodynamics with a superconducting qubit, arXiv:1710.10234 (2017).
- C. Jarzynski and D. K. Wojcik, Classical and Quantum Fluctuation Theorems for Heat Exchange, Phys. Rev. Lett. 92, 230602 (2004).
- A. Rényi, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (University of California, Berkeley, 1961), pp. 547–561.
- T. Van Erven and P. Harremos, Rényi Divergence and Kullback-Leibler Divergence, IEEE Trans. Inf. Theory 60, 3797 (2014).
- S. Beigi, Sandwiched Rényi divergence satisfies data processing inequality, J. Math. Phys. 54, 122202 (2013).
- M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel, On quantum Rényi entropies: A new generalization and some properties, J. Math. Phys. 54, 122203 (2013).
- A. Wehrl, General properties of entropy, Rev. Mod. Phys. 50, 221 (1978).
- W. Yang, W. L. Ma, and R. B. Liu, Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths, Rep. Prog. Phys. 80, 016001 (2017).
- B. B. Wei and R. B. Liu, Lee-Yang Zeros and Critical Times in Decoherence of a Probe Spin Coupled to a Bath, Phys. Rev. Lett. 109, 185701 (2012).
- B. B. Wei, S. W. Chen, H. C. Po, and R. B. Liu, Phase transitions in the complex plane of a physical parameter, Sci. Rep. 4, 5202 (2014).
- B. B. Wei, Z. F. Jiang, and R. B. Liu, Thermodynamic holography, Sci. Rep. 5, 15077 (2015).
- X. H. Peng, H. Zhou, B. B. Wei, J. Y. Cui, J. F. Du, and R. B. Liu, Experimental Observation of Lee-Yang Zeros, Phys. Rev. Lett. 114, 010601 (2015).
- N. Ananikian and R. Kenna, Imaginary magnetic fields in the real world, Physics 8, 2 (2015).
- B. B. Wei, Probing Yang-Lee edge singularity by central spin decoherence, New J. Phys. 19, 083009 (2017).
- B. B. Wei, Probing conformal invariant of non-unitary two-dimensional system by central spin decoherence, Sci. Rep. 8, 3080 (2018).
- J. Goold, U. Poschinger, and K. Modi, Measuring heat exchange of a quantum process, Phys. Rev. E 90, 020101 (2014).
