Continuous-Time Random Walks at All Times

TL;DR

This paper introduces a new theoretical approach using generalized master equations to analyze continuous-time random walks (CTRW) at all times, providing explicit expressions for dynamic quantities beyond stationary states.

Contribution

The paper develops a generalized master equation framework that enables explicit analysis of CTRW dynamics at all times, including non-stationary regimes and specific models.

Findings

Explicit Laplace transform expressions for CTRW dynamics

Effective description of CTRW at all times

Analysis of approach to stationary states and fluctuations

Abstract

Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach, based on generalized master equations picture, that allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specific calculations are performed for homogeneous, periodic models and for CTRW with irreversible detachments. The approach to stationary states for CTRW is analyzed. Our results are also used to analyze generalized fluctuations theorem.