TY  - JOUR
A1  - Hou, Ru
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
A1  - Akimoto, Takuma
T1  - Biased continuous-time random walks for ordinary and equilibrium cases
T2  - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2  - We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent alpha are considered for the WTD psi(t) similar to 1/t(1+alpha). We treat continuous-time random walks (CTRWs) with 0 < alpha < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < alpha < 2 and alpha > 2. We demonstrate that in the presence of a drift CTRWs with alpha < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < alpha < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with alpha > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < alpha < 2 and alpha > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with alpha > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent alpha.
Y1  - 2018
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/52151
SN  - 1463-9076
SN  - 1463-9084
VL  - 20
IS  - 32
SP  - 20827
EP  - 20848
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  -