A minimal model with stochastically broken reciprocity

TL;DR

This paper introduces a minimal stochastic two-body model with broken reciprocity, analyzing its statistical behaviors, energy dynamics, and effective temperature, revealing novel effects on motion and thermodynamics.

Contribution

It presents a new minimal model incorporating stochastic reciprocity violation and explores its impact on system dynamics and thermodynamic properties.

Findings

Velocity and position fluctuations are characterized.

Energy gain and entropy production are analyzed.

Effective temperature of the system is derived.

Abstract

We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity (i.e., random violation of Newton's third law) and then investigate its statistical behaviors, including fluctuations of velocity and position, time evolution of probability distribution functions, energy gain, and entropy production. The effective temperature of this two-body system immersed in a thermal bath is also derived. Furthermore, we heuristically present an extremely minimal model where the relative motion adheres to the same rules as in classical mechanics, while the effect of stochastically broken reciprocity only manifests in the fluctuating motion of the center of mass.