Breymann Wolfgang, Tel Tamas, Vollmer Jurgen
Institute of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland andOlsen & Associates, Seefeldstrasse 233, CH-8008 Zurich, Switzerland.
Chaos. 1998 Jun;8(2):396-408. doi: 10.1063/1.166322.
We review recent results concerning entropy balance in low-dimensional dynamical systems modeling mass (or charge) transport. The key ingredient for understanding entropy balance is the coarse graining of the local phase-space density. It mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected up to a finite resolution. In addition, we derive a new relation for the rate of irreversible entropy production in steady states of dynamical systems: It is proportional to the average growth rate of the local phase-space density. Previous results for the entropy production in steady states of thermostated systems without density gradients and of Hamiltonian systems with density gradients are recovered. As an extension we derive the entropy balance of dissipative systems with density gradients valid at any instant of time, not only in stationary states. We also find a condition for consistency with thermodynamics. A generalized multi-Baker map is used as an illustrative example. (c) 1998 American Institute of Physics.
我们回顾了近期关于低维动力学系统中质量（或电荷）传输建模的熵平衡的研究成果。理解熵平衡的关键要素是局部相空间密度的粗粒化。它模拟了这样一个事实，即由混沌动力学引起的不断细化的相空间结构只能在有限分辨率下被检测到。此外，我们推导出了动力学系统稳态下不可逆熵产生率的一个新关系：它与局部相空间密度的平均增长率成正比。恢复了先前关于无密度梯度的恒温系统和有密度梯度的哈密顿系统稳态下熵产生的结果。作为一个扩展，我们推导出了具有密度梯度的耗散系统在任何时刻（不仅是稳态）都有效的熵平衡。我们还找到了与热力学一致性的一个条件。一个广义多贝克映射被用作说明性示例。（c）1998美国物理研究所。
