标题： 具有非平衡稳态的动能兰格缪尔过程的L2几何遍历性 显示英文标题

标题： L2 geometric ergodicity for the kinetic Langevin process with non-equilibrium steady states

摘要： 在非平衡统计物理模型中，过程的不变测度$\mu$没有明确的密度。 特别是，生成元$L$在$L^2(\mu)$中的伴随算子$L^*$是未知的，并且在这种情况下许多经典技术失效。 在 [5] 中已经取得了重要进展，在较为一般的条件下得到了动理学方程非显式定态的函数不等式。 然而在 [5] 的动理学情形下，几何遍历性仅从具有保守力的情况（对应于显式定态）的函数不等式推导得出。 在这篇短文中，我们在非平衡情形下获得了$L^2$收敛速度。 显示英文摘要

摘要： In non-equilibrium statistical physics models, the invariant measure $\mu$ of the process does not have an explicit density. In particular the adjoint $L^*$ in $L^2(\mu)$ of the generator $L$ is unknown and many classical techniques fail in this situation. An important progress has been made in [5] where functional inequalities are obtained for non-explicit steady states of kinetic equations under rather general conditions. However in [5] in the kinetic case the geometric ergodicity is only deduced from the functional inequalities for the case with conservative forces, corresponding to explicit steady states. In this note we obtain $L^2$ convergence rates in the non-equilibrium case.