Entropic and gradient flow formulations for nonlinear diffusion
Entropic and gradient flow formulations for nonlinear diffusion
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DOI：
10.1063/1.4960748
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发表时间：
2016-08-01
影响因子：
1.3
通讯作者：
Zimmer, Johannes
中科院分区：
文献类型：
--
作者：
Dirr, Nicolas;Stamatakis, Marios;Zimmer, Johannes
考虑了一类非线性扩散偏导数(T)Rho=Delta(Phi(Rho))。结果表明，对于合适的phi，相应的Lyapunov泛函可以解释为热力学熵。这些信息被用来推导出一个相关的度量，这里称为热力学度量。分析仅限于可作为零程过程的水动力极限的非线性扩散。热力学设置与基本零程过程的大偏差原理和相应的脉动流体力学方程相关联。对于后一种连接，热力学度规起着核心作用。由AIP出版公司出版。
Nonlinear diffusion partial derivative(t)rho = Delta(Phi(rho)) is considered for a class of nonlinearities Phi. It is shown that for suitable choices of Phi, an associated Lyapunov functional can be interpreted as thermodynamic entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role. Published by AIP Publishing.