We apply Gamma calculus to the hypoelliptic and non-symmetric setting of Langevin dynamics under general conditions on the potential. This extension allows us to provide explicit estimates on the convergence rate (which is exponential) to equilibrium for the dynamics in a weighted \(H^1(\mu )\) sense, \(\mu \) denoting the unique invariant probability measure of the system. The general result holds for singular potentials, such as the well-known Lennard–Jones interaction and confining well, and it is applied in such a case to estimate the rate of convergence when the number of particles N in the system is large.

中文翻译：

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维拉尼之外的伽马微积分和具有奇异势的朗之万动力学的显式收敛估计

我们将 Gamma 演算应用于一般条件下的 Langevin 动力学的亚椭圆和非对称设置。这种扩展允许我们在加权\(H^1(\mu )\)意义上提供对动态平衡的收敛速率（指数）的明确估计，\(\mu \)表示唯一不变的概率度量系统的。一般结果适用于奇异势，例如众所周知的 Lennard-Jones 相互作用和约束井，并且在这种情况下应用它来估计系统中粒子数N较大时的收敛速度。