论文标题
非排定扩散的熵产生的大型和消失的噪声限制
The large-time and vanishing-noise limits for entropy production in nondegenerate diffusions
论文作者
论文摘要
我们研究了与形式的随机微分方程相关的熵生产功能的行为其中$ b $是全球lipschitz非保守矢量场，使系统无法平衡，重点是较大的限制，然后是消失的噪声限制。家庭的不同成员对应于边界项的不同选择。我们的分析得出了大量定律和局部大偏差原理，这不取决于边界项的选择，并且表现出Gallavotti-Cohen对称性。我们使用来自半群的理论和半经典分析理论的技术来减少功能的渐近行为的描述，以研究无限发电机在$ v $临界点接近的无限发生器变形的二次变形的领先特征值的研究。
We investigate the behaviour of a family of entropy production functionals associated to stochastic differential equations of the form $\mathrm{d} X_s = -\nabla V(X_s) \, \mathrm{d} s + b(X_s) \, \mathrm{d} s + \sqrt{2ε} \, \mathrm{d} W_s $, where $b$ is a globally Lipschitz nonconservative vector field keeping the system out of equilibrium, with emphasis on the large-time limit and then the vanishing-noise limit. Different members of the family correspond to different choices of boundary terms. Our analysis yields a law of large numbers and a local large deviation principle which does not depend on the choice of boundary terms and which exhibits a Gallavotti--Cohen symmetry. We use techniques from the theory of semigroups and from semiclassical analysis to reduce the description of the asymptotic behaviour of the functional to the study of the leading eigenvalue of a quadratic approximation of a deformation of the infinitesimal generator near critical points of $V$.
