Ergodic Measure and Potential Control of Anomalous Diffusion.
Entropy (Basel)
; 25(7)2023 Jun 30.
Article
em En
| MEDLINE
| ID: mdl-37509959
ABSTRACT
In statistical mechanics, the ergodic hypothesis (i.e., the long-time average is the same as the ensemble average) accompanying anomalous diffusion has become a continuous topic of research, being closely related to irreversibility and increasing entropy. While measurement time is finite for a given process, the time average of an observable quantity might be a random variable, whose distribution width narrows with time, and one wonders how long it takes for the convergence rate to become a constant. This is also the premise of ergodic establishment, because the ensemble average is always equal to the constant. We focus on the time-dependent fluctuation width for the time average of both the velocity and kinetic energy of a force-free particle described by the generalized Langevin equation, where the stationary velocity autocorrelation function is considered. Subsequently, the shortest time scale can be estimated for a system transferring from a stationary state to an effective ergodic state. Moreover, a logarithmic spatial potential is used to modulate the processes associated with free ballistic diffusion and the control of diffusion, as well as the minimal realization of the whole power-law regime. The results presented suggest that non-ergodicity mimics the sparseness of the medium and reveals the unique role of logarithmic potential in modulating diffusion behavior.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Entropy (Basel)
Ano de publicação:
2023
Tipo de documento:
Article
País de afiliação:
China