Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
复制标题
离散空间上平均场动力学的熵曲率和收敛到平衡
DOI：
10.30757/alea.v17-18
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发表时间：
2019
影响因子：
0.7
通讯作者：
A. Schlichting
中科院分区：
文献类型：
--
作者：
Matthias Erbar;M. Fathi;A. Schlichting
我们考虑离散空间上粒子系统的平均场极限所引起的非线性演化方程。我们调查的曲率界限的概念，这些动态的自由能的凸性沿着插值在离散运输距离相关的梯度流结构的动态。这个概念扩展了Erbar和Maas研究的线性马尔可夫链动力学。我们表明，正曲率界需要几个功能的不平等控制的动态收敛到平衡。我们建立明确的曲率界限的几个例子的平均场极限的各种经典模型从统计力学。
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a discrete transportation distance related to the gradient flow structure of the dynamics. This notion extends the one for linear Markov chain dynamics studied by Erbar and Maas. We show that positive curvature bounds entail several functional inequalities controlling the convergence to equilibrium of the dynamics. We establish explicit curvature bounds for several examples of mean-field limits of various classical models from statistical mechanics.
影响因子：
1.4
作者：
Grosskinsky S
通讯作者：
Grosskinsky S