We focus on the asymmetry of the interaction in the optimal velocity (OV) model, which is a model of self-driven particles, and analytically investigate the effects of the asymmetry on the fluctuation-response relation, which is one of the remarkable relationships in statistical physics. By linearizing a modified OV model, i.e., the backward-looking optimal velocity model, which can easily control the magnitude of asymmetry in the interaction, we derive $n$ coupled linear oscillators with asymmetric interactions. We analytically solve the equations of the $n$ coupled linear oscillators and calculate the response and correlation functions. We find that the fluctuation response relation does not hold in the $n$ coupled linear oscillators with asymmetric interactions. Moreover, as the magnitude of the asymmetry increases, the difference between the response and correlation functions increases .

• Received 1 April 2020
• Revised 6 June 2020
• Accepted 10 July 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012150

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society