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    Hamiltonian Thermodynamics

    Received 21 September 2020; accepted 27 November 2020

    2020, Vol. 16, no. 4, pp.  557-580

    Author(s): Rashkovskiy S. A.

    It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the Hamiltonian systems considered, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.
    Keywords: Hamiltonian system, adiabatic invariants, thermodynamics, temperature, heat, entropy, thermodynamic processes, the first and second laws of thermodynamics
    Citation: Rashkovskiy S. A., Hamiltonian Thermodynamics, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 4, pp.  557-580

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