Unitary Proof of the Second Law of Thermodynamics

  • Takahiro Sagawa
Part of the Springer Theses book series (Springer Theses)


In this chapter, we review how to derive the second law of thermodynamics for systems that obey quantum mechanics at the microscopic level. Starting with the statement of the second law, we derive it based on quantum statistical mechanics [1, 2, 3, 4, 5]. We formulate the theory such that the total system of the thermodynamic system and the heat baths obey the unitary evolution, and assume that the initial states of the heat baths are in the canonical distribution. Mathematically, our derivation is based on the Klein inequality (or equivalently, the positivity of the quantum relative entropy). The reason why the second law can be derived from the reversible unitary evolution is due to the fact that we select the canonical distributions as the initial states.


Heat Bath External Parameter Helmholtz Free Energy Unitary Evolution Thermodynamic System 
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Copyright information

© Springer Japan 2012

Authors and Affiliations

  1. 1.Kyoto UniversityKyotoJapan

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