The Hamiltonian theory of thermodynamics for reversible and irreversible processes is presented in detail. Particularly, it is demonstrated that non-linear molecular dynamics and thermodynamics of equilibrium and non-equilibrium processes can merge in a single dynamical theory by constructing a homogeneous of first degree in momenta Hamiltonian function on the extended thermodynamic state space and in the entropy representation. The geometrical properties of the physical equilibrium state manifold are discussed and results of numerical experiments with the Hénon–Heiles model that dissipates in a simple thermodynamic system with multiple friction parameters are presented. It is well known that this classical paradigm carries most of the non-linear dynamical characteristics of generic molecular systems. The construction of homogeneous Hamiltonians for composite thermodynamic systems is also outlined in the appendixes, where the theory of Hamiltonian thermodynamics is developed in current differential geometry terms.

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扩展相空间中的哈密顿热力学：非线性分子动力学和经典热力学的统一理论

详细介绍了可逆和不可逆过程的热力学哈密顿理论。特别是，通过在扩展的热力学状态空间和熵表示中构造动量哈密顿函数的一阶齐次，证明了平衡和非平衡过程的非线性分子动力学和热力学可以合并为一个单一的动力学理论。讨论了物理平衡状态流形的几何特性，并介绍了在具有多个摩擦参数的简单热力学系统中耗散的 Hénon-Heiles 模型的数值实验结果。众所周知，这种经典范式具有一般分子系统的大部分非线性动力学特征。