Run-and-tumble dynamics with non-reciprocal transitions between three velocity states

TL;DR

This paper explores how non-reciprocal transition rates between three velocity states in active particles lead to diverse non-equilibrium transport behaviors, including ballistic motion and giant diffusion, through analytical and simulation methods.

Contribution

It introduces a minimal three-state run-and-tumble model with non-reciprocal transitions, revealing new non-equilibrium transport phenomena and exact expressions for key transport metrics.

Findings

Identification of a transition-rate manifold with diffusive behavior

Exact formulas for drift and diffusion coefficients

Demonstration of non-Gaussian transients and giant diffusion

Abstract

We investigate the transport properties of active particles undergoing a three-state run-and-tumble dynamics in one dimension, induced by non-reciprocal transition rates between self-propelling velocity states $\{-v, 0, +v\}$ that explicitly break microscopic reversibility. Departing from conventional reciprocal models, our formulation introduces a minimal yet rich framework for studying non-equilibrium transport driven by internal state asymmetries. Using kinetic Monte Carlo simulations and analytical methods, we characterize the particle's transport properties across the transition-rates space. The model exhibits a variety of non-equilibrium behaviors, including ballistic transport, giant diffusion, and Gaussian or non-Gaussian transients, depending on the degree of asymmetry in the transition rates. We identify a manifold in transition-rate space where long-time diffusive behavior emerges despite the absence of microscopic reversibility. Exact expressions are obtained for the drift, effective diffusion coefficient, and moments of the position distribution. Our results establish how internal-state irreversibility governs macroscopic transport, providing a tractable framework to study non-equilibrium active motion beyond reciprocal dynamics.