论文标题
通过信息伽玛演算的熵耗散：非可逆随机微分方程
Entropy dissipation via Information Gamma calculus: Non-reversible stochastic differential equations
论文作者
论文摘要
我们制定明确的界限，以确保某些非梯度随机微分方程对其不变分布的指数耗散。我们的方法在$ l^2 $ - Wasserstein Space中扩展了Gamma微积分和Hessian运营商之间的连接。从详细的角度来看，我们在概率空间中应用Lyapunov方法，其中选择Lyapunov功能作为相对Fisher信息。我们得出Fisher信息引起的伽马积分来处理非梯度漂移载体场。我们获得了按$ L_1 $距离限制的显式耗散，并制定了不可逆的Poincar {é}不等式。提供了一个非可逆兰格文动态的分析示例。
We formulate explicit bounds to guarantee the exponential dissipation for some non-gradient stochastic differential equations towards their invariant distributions. Our method extends the connection between Gamma calculus and Hessian operators in $L^2$--Wasserstein space. In details, we apply Lyapunov methods in the space of probabilities, where the Lyapunov functional is chosen as the relative Fisher information. We derive the Fisher information induced Gamma calculus to handle non-gradient drift vector fields. We obtain the explicit dissipation bound in terms of $L_1$ distance and formulate the non-reversible Poincar{é} inequality. An analytical example is provided for a non-reversible Langevin dynamic.
