Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon.

摘要: The trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance position grows much faster than its mean. A description dynamics by moments is therefore not informative. Instead, we propose and analyze local directly measurable characteristics, which overcome this limitation. We discuss most probable (position maximum probability density) uncertainty cubic potential, $V(x)\ensuremath{\sim}{x}^{3}$, both transient regime long-time limit. shifts against acting force as function time temperature. Simultaneously, does increase observable shift. In limit, density naturally attains quasistationary form. interpret process stabilization via measurement-feedback mechanism, Maxwell demon, works entropy pump. rules for measurement feedback arise from basic properties dynamics. All reported effects are inherent any system. Their detailed understanding will stimulate development stochastic engines amplifiers and, later, their quantum counterparts.