Quantum Bochkov-Kuzovlev work fluctuation theorems

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 369, Issue 1935, 2011, Pages 291-306

  Campisi, Michele ^a   Talkner, Peter ^a   Hänggi, Peter ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Entropy; Fluctuations; Non equilibrium; Nonlinear response; Thermodynamics; Work

Indexed keywords

BIOELECTRIC PHENOMENA; ENTROPY; QUANTUM ELECTRONICS; QUANTUM OPTICS;

EXTERNAL ACTION; EXTERNAL WORK; FLUCTUATIONS; INTERNAL ENERGIES; NON EQUILIBRIUM; NON-LINEAR RESPONSE; QUANTUM FLUCTUATION; QUANTUM SYSTEM; WORK; WORK-FLUCTUATION THEOREM;

THERMODYNAMICS;

EID: 79251526554     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2010.0252     Document Type: Article

References (42)

1. Callen, H. B. & Welton, T. A. 1951 Irreversibility and generalized noise. Phys. Rev. 83, 34-40. (doi:10.1103/PhysRev.83.34)
2. Green, M. S. 1952 Markoff random processes and the statistical mechanics of time-dependent phenomena. J. Chem. Phys. 20, 1281. (doi:10.1063/1.1700722)
3. Kubo, R. 1957 Statistical mechanical theory of irreversible processes I. J. Phys. Soc. Jpn 12, 570-586. (doi:10.1143/JPSJ.12.570)
4. Einstein, A. 1926 Investigations on the theory of Brownian movement. London, UK: Methuen. (Reprinted by Dover 1956.)
5. Johnson, J. B. 1928 Thermal agitation of electricity in conductors. Phys. Rev. 32, 97-109. (doi:10.1103/PhysRev.32.97)
6. Nyquist, H. 1928 Thermal agitation of electric charge in conductors. Phys. Rev. 32, 110-113. (doi:10.1103/PhysRev.32.110)
7. Hänggi, P. & Thomas, H. 1982 Stochastic processes: time-evolution, symmetries and linear response. Phys. Rep. 88, 207-319. (doi:10.1016/0370-1573(82)90045-X)
8. Bochkov, G. N. & Kuzovlev, Y. E. 1977 General theory of thermal fluctuations in nonlinear systems. Sov. Phys. JETP 45, 125-130. (Zh. Eksp. Theor. Fiz. 72, 238-247.)
9. Bochkov, G. N. & Kuzovlev, Y. E. 1981 Nonlinear fluctuation- dissipation relations and stochastic models in nonequilibrium thermodynamics I. Generalized fluctuation-dissipation theorem. Physica A 106, 443-479. (doi:10.1016/0378-4371(81)90122-9)
10. Jarzynski, C. 1997 Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690-2693. (doi:10.1103/PhysRevLett.78.2690)
11. Jarzynski, C. & Horowitz, J. 2007 Comparison of work fluctuation relations. J. Stat. Mech. P11002. (doi:10.1088/1742-5468/2007/11/P11002)
12. Jarzynski, C. 2007 Comparison of far-from-equilibrium work relations. C. R. Phys. 8, 495-506. (doi:10.1016/j.crhy.2007.04.010)
13. Allahverdyan, A. E. & Nieuwenhuizen, T. M. 2005 Fluctuations of work from quantum subensembles: the case against quantum work-fluctuation theorems. Phys. Rev. E 71, 066102. (doi:10.1103/PhysRevE.71.066102) (Pubitemid 41663817)
14. Talkner, P., Lutz, E. & Hänggi, P. 2007 Fluctuation theorems: work is not an observable. Phys. Rev. E 75, 050102(R). (doi:10.1103/PhysRevE.75. 050102) (Pubitemid 47000998)
15. Campisi, M., Talkner, P. & Hänggi, P. 2009 Fluctuation theorem for arbitrary open quantum systems. Phys. Rev. Lett. 102, 210401. (doi:10.1103/PhysRevLett.102.210401)
16. Talkner, P., Campisi, M. & Hänggi, P. 2009 Fluctuation theorems in driven open quantum systems. J. Stat. Mech. 2009, P02025. (doi:10.1088/1742-5468/2009/02/P02025)
17. Talkner, P. & Hänggi, P. 2007 The Tasaki-Crooks quantum fluctuation theorem. J. Phys. A 40, F569-F571. (doi:10.1088/1751-8113/40/26/F08)
18. Talkner, P., Hänggi, P. & Morillo, M. 2008 Microcanonical quantum fluctuation theorem. Phys. Rev. E 77, 051131. (doi:10.1103/PhysRevE.77. 051131)
19. Andrieux, D., Gaspard, P., Monnai, T. & Tasaki, S. 2009 The fluctuation theorem for currents in open quantum systems. New J. Phys. 11, 043014. (doi:10.1088/1367-2630/11/4/043014)
20. Messiah, A. 1962 Quantum mechanics. Amsterdam, The Netherlands: North-Holland.
21. Campisi, M., Talkner, P. & Hänggi, P. 2010 Fluctuation theorems for continuously monitored quantum fluxes. Phys. Rev. Lett. 105, 140601. (doi:10.1103/PhysRevLett.105.140601)
22. Cleuren, B., Van den Broeck, C. & Kawai, R. 2006 Fluctuation and dissipation of work in a Joule experiment. Phys. Rev. Lett. 96, 050601. (doi:10.1103/PhysRevLett.96.050601) (Pubitemid 43270970)
23. Gibbs, J. 1902 Elementary principles in statistical mechanics. Yale, CT: Yale University Press. (Reprinted by Dover 1960.)
24. Campisi, M. 2005 On the mechanical foundations of thermodynamics: the generalized Helmholtz theorem. Stud. Hist. Phil. Mod. Phys. 36, 275-290. (doi:10.1016/j.shpsb.2005.01.001) (Pubitemid 40717234)
25. Campisi, M. 2008 Statistical mechanical proof of the second law of thermodynamics based on volume entropy. Stud. Hist. Phil. Mod. Phys. 39, 181-194. (doi:10.1016/j.shpsb.2007.09.002)
26. Campisi, M. & Kobe, D. H. 2010 Derivation of the Boltzmann principle. Am. J. Phys. 78, 608-615. (doi:10.1119/1.3298372)
27. Dunkel, J. & Hilbert, S. 2006 Phase transitions in small systems: microcanonical vs. canonical ensembles. Physica A 370, 390-406. (doi:10.1016/j.physa.2006.05.018) (Pubitemid 44310888)
28. Hertz, P. 1910 Über die mechanischen Grundlagen der Thermodynamik. Ann. Phys. 338, 225-274. (doi:10.1002/andp.19103381202)
29. Hertz, P. 1910 Über die mechanischen Grundlagen der Thermodynamik. Ann. Phys. 338, 537-552. (doi:10.1002/andp.19103381305)
30. Pearson, E. M., Halicioglu, T. & Tiller, W. A. 1985 Laplace-transform technique for deriving thermodynamic equations from the classical microcanonical ensemble. Phys. Rev. A 32, 3030-3039. (doi:10.1103/PhysRevA.32. 3030)
31. Schlüter, A. 1948 Zur Statistik klassischer Gesamtheiten. Z. Naturforsch. 3A, 350-360. [Transl., see http://people.chem.byu.edu/rbshirts/ research/schluter1948translation.doc].
32. Einstein, A. 1911 Bemerkungen zu den P. Hertzschen Arbeiten: 'Über die mechanischen Grundlagen der Thermodynamik'. Ann. Phys. 339, 175-176. (doi:10.1002/andp.19113390111)
33. Ruelle, D. 1969 Statistical mechanics. New York, NY: W. A. Benjamin.
34. Andrieux, D. & Gaspard, P. 2008 Quantum work relations and response theory. Phys. Rev. Lett. 100, 230404. (doi:10.1103/PhysRevLett.100.230404)
35. Cohen, E. G. D. & Mauzerall, D. 2005 The Jarzynski equality and the Boltzmann factor. Mol. Phys. 103, 2923-2926. (doi:10.1080/00268970500151536) (Pubitemid 43175264)
36. Kawai, R., Parrondo, J. M. R. & Van den Broeck, C. 2007 Dissipation: the phase-space perspective. Phys. Rev. Lett. 98, 080602. (doi:10.1103/ PhysRevLett.98.080602) (Pubitemid 46326134)
37. Vaikuntanathan, S. & Jarzynski, C. 2009 Dissipation and lag in irreversible processes. EPL 87, 60005. (doi:10.1209/0295-5075/87/60005)
38. Schleich, W. P. 2001 Quantum optics in phase space. Berlin, Germany: Wiley.
39. Talkner, P., Burada, P. S. & Hänggi, P. 2008 Statistics of work performed on a forced quantum oscillator. Phys. Rev. E 78, 011115. (doi:10.1103/PhysRevE.78.011115)
40. Talkner, P., Burada, P. S. & Hänggi, P. 2009 Erratum: statistics of work performed on a forced quantum oscillator. Phys. Rev. E. 79, 039902. (doi:10.1103/PhysRevE.79.039902)
41. Campisi, M. 2008 Increase of Boltzmann entropy in a forced harmonic oscillator. Phys. Rev. E 78, 051123. (doi:10.1103/PhysRevE.78.051123)
42. Husimi, K. 1953 Miscellanea in elementary quantum mechanics, II. Prog. Theor. Phys. 9, 381-402. (doi:10.1143/PTP.9.381)