By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We completely clarify its qualitative dynamics, the underlying geometrical structures and we also show how to apply discrete gradient methods to numerically integrate the evolution equations for these systems.

中文翻译：

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具有摩擦的简单热力学系统的接触几何

通过与接触结构相关的雅可比结构，我们使用所谓的演化矢量场来提出具有摩擦的孤立热力学系统的新表征，这是一类简单但重要的热力学系统，它自然满足第一和第二定律热力学，即孤立系统的总能量守恒和不减少的总熵，分别。我们完全阐明了它的定性动力学、潜在的几何结构，我们还展示了如何应用离散梯度方法对这些系统的演化方程进行数值积分。