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Fluctuation Theorems of Work and Entropy in Hamiltonian Systems

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Abstract

Fluctuation theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy change from nonequilibrium processes, they help in our understanding of the second law and the emergence of irreversibility from time-reversible equations of motion at microscopic level. A vast number of such theorems have been proposed in literature, ranging from Hamiltonian to stochastic systems, from systems in steady state to those in transient regime, and for both open and closed quantum systems. In this article, we discuss about a few such relations, when the system evolves under Hamiltonian dynamics.

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Suggested Reading

  1. C Jarzynski, Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale, Annu. Rev. Condens. Matter Phys., 2, 329, 2010.

    Google Scholar 

  2. U Seifert, Stochastic Thermodynamics, Fluctuation Theorems and Molecular Machines, Rep. Prog. Phys., 75, 126001, 2012.

    Article  Google Scholar 

  3. C Bustamante, J Liphardt and F Ritort, The Nonequilibrium Thermodynamics of Small Systems, Physics Today, 58, 43, 2005.

    Article  Google Scholar 

  4. D J Evans, E G D Cohen and G P Morriss, Probability of Second Law Violations in Shearing Steady States, Phys. Rev. Lett., 71, 2401, 1993.

    Article  Google Scholar 

  5. G Gallavotti and E G D Cohen, Dynamical Ensembles in Nonequilibrium Statistical Mechanics, Phys. Rev. Lett., 74, 2694, 1995.

    Article  Google Scholar 

  6. J Kurchan, Fluctuation Theorem for Stochastic Dynamics, J. Phys. A: Math. Gen., 31, 3719, 1998.

    Article  Google Scholar 

  7. J L Lebowitz and H Spohn, A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics, J. Stat. Phys., 95, 333, 1999.

    Article  Google Scholar 

  8. C Jarzynski, Nonequilibrium Equality for Free Energy Differences, Phys. Rev. Lett., 78, 2690, 1997.

    Article  Google Scholar 

  9. G E Crooks, Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences, Phys. Rev. E, 60, 2721, 1999.

    Article  Google Scholar 

  10. D Chandler, Introduction to Modern Statistical Mechanics, Oxford University Press, USA, 1987.

    Google Scholar 

  11. G M Wang, E M Sevick, E Mittag, D J Searles and D J Evans, Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales, Phys. Rev. Lett., 89, 050601, 2002.

    Article  Google Scholar 

  12. J Liphardt, S Dumont, S B Smith, I Tinoco Jr and C Bustamante, Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski’s Equality, Science, 296, 1832, 2002.

    Article  Google Scholar 

  13. R van Zon, S Ciliberto and E G D Cohen, Power and Heat Fluctuation Theorems for Electric Circuits, Phys. Rev. Lett., 92, 130601, 2004.

    Article  Google Scholar 

  14. D Collin, F Ritort, C Jarzynski, S B Smith, I Tinoco Jr and C Bustamante, Veriflcation of the Crooks Fluctuation Theorem and Recovery of RNA Folding Free Energies, Nature, 437, 231, 2005.

    Article  Google Scholar 

  15. U Seifert, Stochastic Thermodynamics: Principles and Perspectives, Eur. Phys. J. B, 64, 423, 2008.

    Article  Google Scholar 

  16. G M Wang, J C Reid, D M Carberry, D R M Williams, E M Sevick and D J Evans, Experimental Study of the Fluctuation Theorem in a Nonequilibrium Steady State, Phys. Rev. E, 71, 046142, 2005.

    Article  Google Scholar 

  17. S Joubaud, N B Garnier and S Ciliberto, Fluctuations of the Total Entropy Production in Stochastic Systems, Europhys. Lett., 82, 30007, 2008.

    Article  Google Scholar 

  18. J Kurchan, arxiv/cond-mat: 0007360.

  19. Y Morikuni and H Tasaki, Quantum Jarzynski-Sagawa-Ueda Relations, J. Stat. Phys., 143, 1, 2010.

    Article  Google Scholar 

  20. M Campisi, P Hänggi and P Talkner, Colloquium: Quantum Fluctuation Relations: Foundations and Applications, Rev. Mod. Phys., 83, 771, 2011.

    Article  Google Scholar 

  21. P Talkner, E Lutz and P Hänggi, Fluctuation Theorems: Work is Not an Observable, Phys. Rev. E, 75, 050102, 2007.

    Article  Google Scholar 

  22. S Lahiri, S Rana and A M Jayannavar, Fluctuation Theorems in the Presence of Information Gain and Feedback, J. Phys. A: Math. Theor., 45, 065002, 2012.

    Article  Google Scholar 

  23. T M Cover and J A Thomas, Elements of Information Theory, Wiley-Interscience, 1991.

    Book  Google Scholar 

  24. M Campisi, P Talkner and P Hänggi, Fluctuation Theorem for Arbitrary Open Quantum Systems, Phys. Rev. Lett., 102, 210401.

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Correspondence to Sourabh Lahiri or Arun M. Jayannavar.

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Sourabh Lahiri is an Assistant Professor at Birla Institute of Technology, Mesra (Ranchi). He works in the field of nonequilibrium statistical mechanics.

Arun M Jayannavar is a senior scientist at Institute of Physics, Bhubaneswar and is interested in general condensed matter physics.

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Lahiri, S., Jayannavar, A.M. Fluctuation Theorems of Work and Entropy in Hamiltonian Systems. Reson 23, 573–589 (2018). https://doi.org/10.1007/s12045-018-0650-y

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  • DOI: https://doi.org/10.1007/s12045-018-0650-y

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