Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation and Linear Response

¹ CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy
² Max-Planck-Institute for Physics of Complex Systems, Noethnitzer Str. 38 D-91187 Dresden, Germany
³ Akhiezer Institute for Theoretical Physics, NSC KIPT, Kharkov 61108, Ukraine
⁴ School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel

^⋆ Corresponding author. E-mail: alessandro.taloni@gmail.com

Abstract

The Generalized Elastic Model is a linear stochastic model which accounts for the behaviour of many physical systems in nature, ranging from polymeric chains to single-file systems. If an external perturbation is exerted only on a single point x^⋆ (tagged probe), it propagates throughout the entire system. Within the fractional Langevin equation framework, we study the effect of such a perturbation, in cases of a constant force applied. We report most of the results arising from our previous analysis and, in the present work, we show that the Fox H-functions formalism provides a compact, elegant and useful tool for the study of the scaling properties of any observable. In particular we show how the generalized Kubo fluctuation relations can be expressed in terms of H-functions.