Maes Christian, Netocný Karel, Shergelashvili Bidzina M
Instituut voor Theoretische Fysica, K.U. Leuven, B-3001 Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011121. doi: 10.1103/PhysRevE.80.011121. Epub 2009 Jul 17.
We investigate the relation between an applied potential and the corresponding stationary-state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for the relative density when the potential is locally perturbed, and inversely, we find that the potential needs to be wholly rearranged for the purpose of creating a locally changed density. The direct question, determining the density as a function of the potential, comes under the response theory out of equilibrium. The inverse problem of determining the potential that produces a given stationary distribution naturally arises in the study of dynamical fluctuations. This link to the fluctuation theory results in a variational characterization of the stationary density upon a given potential and vice versa.
我们研究了非平衡和过阻尼扩散过程中施加电势与相应稳态占据之间的关系。当电势受到局部扰动时，这种关系通常会变得具有长程性，从而导致相对密度发生全局变化。反之，我们发现为了产生局部变化的密度，电势需要进行整体重新排列。确定密度作为电势函数的直接问题属于非平衡响应理论的范畴。在动态涨落研究中自然会出现确定产生给定稳态分布的电势的逆问题。这种与涨落理论的联系导致了给定电势下稳态密度的变分表征，反之亦然。
