Smoluchowski dynamics and the ergodic-nonergodic transition

Ergodic-nonergodic transition in a threshold system with feedback.

A threshold system with feedback is studied from the viewpoint of an ergodic-nonergodic transition, a kind of nonequilibrium phase transition, as the rate of input signal variation is changed. By discussing the time evolution of the distribution function, instead of its lowest moment (an order parameter), we can determine the transition point and make clear the role and limitation of the self-c...

Asymptotic Stability of the Wonham Filter: Ergodic and Nonergodic Signals

The stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the nonergodic case, the stability is implied by identifiability conditions, formulated explicitly in term...

Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long-time behavior of the mean square displacement. Anomalous diffusion is found. Since the diffusion exponent cannot be predicted using a simple scaling argumen...

Facilitated spin models, mode coupling theory, and ergodic–nonergodic transitions

Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking.

Diffusion in the plasma membrane of living cells is often found to display anomalous dynamics. However, the mechanism underlying this diffusion pattern remains highly controversial. Here, we study the physical mechanism underlying Kv2.1 potassium channel anomalous dynamics using single-molecule tracking. Our analysis includes both time series of individual trajectories and ensemble averages. We...