论文标题
气体的最佳热力学过程
Optimal Thermodynamic Processes For Gases
论文作者
论文摘要
在本文中，我们考虑了气体平衡热力学中的最佳控制问题。气体的热力学状态由触点热力学空间中的Legendrian Submanifold给出。使用Pontryagin的最大原理，我们在该亚策略上找到了热力学过程，因此气体可以最大化工作功能。对于理想的气体，该问题在Liouville的意义上被证明是可以整合的，并且其解决方案是通过动作角度变量给出的。对于被认为是理想扰动的真实气体，积分是渐近地给出的。
In this paper, we consider an optimal control problem in equilibrium thermodynamics of gases. 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 on 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 as a perturbation of ideal ones, the integrals are given asymptotically.
