Contact geometry for simple thermodynamical systems with friction

被引:29
|
作者
Anahory Simoes, Alexandre [1 ]
de Leon, Manuel [1 ,2 ]
Lainz Valcazar, Manuel [1 ]
Martin de Diego, David [1 ]
机构
[1] UAM, UCM, UC3M, Inst Ciencias Matemat,CSIC, Calle Nicolas Cabrera,13-15,Campus Cantoblanco, Madrid 28049, Spain
[2] UAM, Real Acad Espanola Ciencias, Calle Nicolas Cabrera,13-15,Campus Cantoblanco, Madrid 28049, Spain
关键词
contact geometry; thermodynamical systems; single bracket formulation; discrete gradient methods; DISCRETE; INTEGRATION;
D O I
10.1098/rspa.2020.0244
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
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页数:16
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