非线性扩散的熵流和梯度流公式
Entropic and gradient flow formulations for nonlinear diffusion
摘要：
研究一类非线性项$Φ$的非线性扩散$\partial_t ρ= Δ(Φ(ρ))$.结果表明，对于适当的选择$Φ$，相关的李雅普诺夫功能可以解释为热力学熵。该信息用于导出相关度量，这里称为热力学度量。分析仅限于非线性扩散可作为零程过程的流体动力学极限。的热力学设置是联系在一起的基础零范围的过程和相应的波动流体动力学方程的大偏差原则。对于后一种联系，热力学度规起着核心作用。
英文摘要：
Nonlinear diffusion $\partial_t ρ= Δ(Φ(ρ))$ is considered for a class of nonlinearities $Φ$. It is shown that for suitable choices of $Φ$, an associated Lyapunov functional can be interpreted as thermodynamics 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.
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