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The Second Law of Thermodynamics at the Microscopic Scale


In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this paper, we investigate how the relaxation toward equilibrium is made possible through interactions that do not lead to significant exchange of energy, and argue for the validity of the second law of thermodynamics at the microscopic scale.

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  1. Popescu, S., Short, A.J., Winter, A.: Entanglement and the foundations of statistical mechanics. Nat. Phys. 2, 754 (2006)

    Article  Google Scholar 

  2. Tasaki, H.: From quantum dynamics to canonical distribution: general picture and a rigorous example. Phys. Rev. Lett. 80, 1373 (1998)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. Gemmer, J., Mahler, G.: Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jayne’s principle. Eur. Phys. J. B 31, 249 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  4. Goldstein, S., Lebowitz, J.L., Tumulka, R., Zanghì, N.: Canonical typicality. Phys. Rev. Lett. 96, 050403 (2006)

    ADS  MathSciNet  Article  Google Scholar 

  5. Bartsch, C., Gemmer, J.: Dynamical typicality of quantum expectation values. Phys. Rev. Lett. 102, 110403 (2009)

    ADS  Article  Google Scholar 

  6. Skrzypczyk, P., Short, A.J., Popescu, S.: Work extraction and thermodynamics for individual quantum systems. Nat. Commun. 5, 4185 (2014)

    ADS  Article  Google Scholar 

  7. Gemmer, J., Mahler, G.: Entanglement and the factorization-approximation. Eur. Phys. J. D 17, 385 (2001)

    ADS  Article  Google Scholar 

  8. Unruh, W.G., Wald, R.M.: Evolution laws taking pure states to mixed states in quantum field theory. Phys. Rev. D 52, 2176 (1995)

    ADS  MathSciNet  Article  Google Scholar 

  9. Unruh, W.G.: Decoherence without dissipation. Phil. Trans. R. Soc. A 370, 4454–4459 (2012)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  10. Perez, A.: No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox. Class. Quantum Grav. 32, 084001 (2015)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  11. Roßnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K., Lutz, E.: Nanoscale heat engine beyond Carnot limit. Phys. Rev. Lett. 112, 030602 (2014)

    ADS  Article  Google Scholar 

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We are grateful to Goffredo Chirco, Tommaso De Lorenzo, Alejandro Perez, and Carlo Rovelli, for interesting discussions and useful comments.

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Correspondence to Thibaut Josset.

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Josset, T. The Second Law of Thermodynamics at the Microscopic Scale. Found Phys 47, 1185–1190 (2017).

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  • Second law of thermodynamics
  • Quantum typicality
  • von Neumann entropy
  • Isolated systems