Kushner Alexei, Lychagin Valentin, Roop Mikhail
Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia.
Department of Mathematics and Informatics, Moscow Pedagogical State University, 1/1 M. Pirogovskaya Str., 119991 Moscow, Russia.
Entropy (Basel). 2020 Apr 15;22(4):448. doi: 10.3390/e22040448.
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.
在本文中，我们考虑气体平衡热力学中的一个最优控制问题。气体的热力学状态由接触热力学空间中的一个勒让德子流形给出。利用庞特里亚金极大值原理，我们在这个子流形中找到一个热力学过程，使得气体的功泛函最大化。对于理想气体，该问题在刘维尔意义下是可积的，其解通过作用 - 角变量给出。对于被视为理想气体微扰的真实气体，积分以渐近形式给出。
