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Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom

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Abstract

Starting from and only using classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike in many of the standard and recent works on the second law, the macroscopic dynamics is not governed by an external action but undergoes the back reaction of the microscopic degrees of freedom. Our theorems cover such physical situations as impact between macroscopic bodies, thermodynamic machines, and molecular motors. Our work identifies and quantifies the physical limitations on the applicability of the second law for small systems.

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Authors and Affiliations

  1. Instituut voor Theoretische Fysica, K.U.Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium

    Christian Maes

  2. Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo, 171-8588, Japan

    Hal Tasaki

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  1. Christian Maes
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  2. Hal Tasaki
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Correspondence to Hal Tasaki.

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Maes, C., Tasaki, H. Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom. Lett Math Phys 79, 251–261 (2007). https://doi.org/10.1007/s11005-006-0136-9

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  • DOI: https://doi.org/10.1007/s11005-006-0136-9

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