Multi-point distribution for Gaussian non-equilibrium non-Markovian observables
Abstract
When analyzing experimental or simulation time-series data, the question arises whether it is possible to tell from a one-dimensional time-dependent trajectory whether the system is in equilibrium or not. We here consider the non-equilibrium version of the generalized Langevin equation for a Gaussian observable and show that i) the multi-point joint distribution solely depends on the two-point correlation function and that ii) the two-point correlation function for a non-equilibrium process is identical to an equilibrium process with uniquely determined parameters. Since the multi-point joint distribution completely characterizes the dynamics of an observable, this means that the non-equilibrium character of a system, in contrast to its non-Markovianity, cannot be read off from a one-dimensional trajectory.
Cite
@article{arxiv.2310.08886,
title = {Multi-point distribution for Gaussian non-equilibrium non-Markovian observables},
author = {Roland R Netz},
journal= {arXiv preprint arXiv:2310.08886},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2310.00748