Abstract
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.
Similar content being viewed by others
References
Popescu, S., Short, A.J., Winter, A.: Entanglement and the foundations of statistical mechanics. Nat. Phys. 2, 754 (2006)
Tasaki, H.: From quantum dynamics to canonical distribution: general picture and a rigorous example. Phys. Rev. Lett. 80, 1373 (1998)
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)
Goldstein, S., Lebowitz, J.L., Tumulka, R., Zanghì, N.: Canonical typicality. Phys. Rev. Lett. 96, 050403 (2006)
Bartsch, C., Gemmer, J.: Dynamical typicality of quantum expectation values. Phys. Rev. Lett. 102, 110403 (2009)
Skrzypczyk, P., Short, A.J., Popescu, S.: Work extraction and thermodynamics for individual quantum systems. Nat. Commun. 5, 4185 (2014)
Gemmer, J., Mahler, G.: Entanglement and the factorization-approximation. Eur. Phys. J. D 17, 385 (2001)
Unruh, W.G., Wald, R.M.: Evolution laws taking pure states to mixed states in quantum field theory. Phys. Rev. D 52, 2176 (1995)
Unruh, W.G.: Decoherence without dissipation. Phil. Trans. R. Soc. A 370, 4454–4459 (2012)
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)
Roßnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K., Lutz, E.: Nanoscale heat engine beyond Carnot limit. Phys. Rev. Lett. 112, 030602 (2014)
Acknowledgements
We are grateful to Goffredo Chirco, Tommaso De Lorenzo, Alejandro Perez, and Carlo Rovelli, for interesting discussions and useful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Josset, T. The Second Law of Thermodynamics at the Microscopic Scale. Found Phys 47, 1185–1190 (2017). https://doi.org/10.1007/s10701-017-0104-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-017-0104-5