Nonlinear physics and mechanics
S. A. Rashkovskiyab
a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences,
prosp. Vernadskogo 101/1, Moscow, 119526 Russia
b Tomsk State University,
ul. Lenina 36, Tomsk, 634050 Russia
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.
Hamiltonian system, adiabatic invariants, thermodynamics, temperature, heat, entropy, thermodynamic processes, the first and second laws of thermodynamics
|Ministry of Education and Science of the Russian Federation
|This work was carried out in accordance with the State Assignment No. AAAA-A20-120011690135-5.
Funding was provided in part by the Tomsk State University Competitiveness Improvement Program.
PDF file (390 kB)
MSC: 70H05, 70H11, 70H12, 70K70
S. A. Rashkovskiy, “Hamiltonian Thermodynamics”, Rus. J. Nonlin. Dyn., 16:4 (2020), 557–580
Citation in format AMSBIB
\by S. A. Rashkovskiy
\paper Hamiltonian Thermodynamics
\jour Rus. J. Nonlin. Dyn.
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