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Optimal Thermodynamic Processes For Gases

1
Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia
2
Department of Mathematics and Informatics, Moscow Pedagogical State University, 1/1 M. Pirogovskaya Str., 119991 Moscow, Russia
3
V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, Russia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 448; https://doi.org/10.3390/e22040448
Received: 4 March 2020 / Revised: 3 April 2020 / Accepted: 13 April 2020 / Published: 15 April 2020
(This article belongs to the Special Issue Thermodynamics, Geometry and Control Theory)
In this paper, we consider an optimal control problem in the equilibrium thermodynamics of gases. The thermodynamic state of the gas is given by a Legendrian submanifold in a contact thermodynamic space. Using Pontryagin’s maximum principle, we find a thermodynamic process in this submanifold such that the gas maximizes the work functional. For ideal gases, this problem is shown to be integrable in Liouville’s sense and its solution is given by means of action-angle variables. For real gases considered to be a perturbation of ideal ones, the integrals are given asymptotically. View Full-Text
Keywords: measurement; information gain; real gases; optimal control; Pontryagin’s maximum principle; Hamiltonian systems; action-angle variables; asymptotical methods measurement; information gain; real gases; optimal control; Pontryagin’s maximum principle; Hamiltonian systems; action-angle variables; asymptotical methods
MDPI and ACS Style

Kushner, A.; Lychagin, V.; Roop, M. Optimal Thermodynamic Processes For Gases. Entropy 2020, 22, 448.

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