Abstract We solve an optimal control problem for thermodynamic processes in an ideal gas. The thermodynamic state is given by a Legendrian manifold in a contact space. Pontryagin’s maximum principle is used to find an optimal trajectory (thermodynamic process) on this manifold that maximizes the work of the gas. In the case of ideal gases, it is shown that the corresponding Hamiltonian system is completely integrable and its quadrature-based solution is given. Keywords : contact geometry, thermodynamics, optimal control, Hamiltonian systems, integrability

中文翻译：

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气体热力学过程优化控制中的接触几何

摘要 我们解决了理想气体中热力学过程的最优控制问题。热力学状态由接触空间中的勒让德流形给出。庞特里亚金的最大值原理用于在该流形上找到使气体做功最大化的最佳轨迹（热力学过程）。在理想气体的情况下，证明了相应的哈密顿系统是完全可积的，并给出了其基于正交的解。关键词：接触几何，热力学，最优控制，哈密顿系统，可积性