论文标题
哈密顿热力学
Hamiltonian thermodynamics
论文作者
论文摘要
人们认为，热力学定律与系统中发生的随机过程有关，因此，在热力学方法的框架内无法描述确定性的机械系统。在本文中，我们表明热力学（或更确切地说，更确切地说是热力学的描述）即使是针对确定性的哈密顿系统（例如，只有一种自由度）也可以构建。我们表明，对于此类系统，可以引入热能，温度，熵，Helmholtz自由能等的类似物，它们通过通常的热力学关系相互关联。对于被考虑的哈密顿系统，热力学的第一和第二定律是严格衍生的，其形式与普通（分子）热力学相同。结果表明，对于哈密顿系统，可以介绍热力学状态的概念，热力学过程和热力学循环，特别是卡诺循环，这些循环用与通常的热力学类似物相同的关系描述。
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 considered Hamiltonian systems, 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.
