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  • Open Access

Ergodicity breaking in active run-and-tumble particles in a double-well potential

Urna Basu1,*, Satya N. Majumdar2, and Alberto Rosso2

  • *Contact author: urna@bose.res.in
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APS Open Sci. 1, 000021 – Published 18 May, 2026

DOI: https://doi.org/10.1103/jysw-w2mb

Abstract

We investigate the dynamics of a run-and-tumble particle in a double-well potential and demonstrate that, in stark contrast to Brownian particles, active dynamics can lead to strong ergodicity breaking. When the barrier height exceeds a critical threshold, the long-time position distribution depends crucially on the initial condition: If the particle starts within the basin of attraction of one well, it remains trapped there, while if it begins between the two basins, it can reach either well with a finite probability, which we compute exactly via hitting probabilities. Below the critical barrier height, ergodicity is restored and the system converges to a unique stationary distribution, which we derive analytically. Using this result, we also estimate the characteristic barrier-crossing time and show that it violates Kramers-Arrhenius law and displays a divergence near the critical height following a Vogel-Fulcher-Tammann-like form with an anomalous exponent 1/2.

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Outline

Information

APS Open Sci. 1, 000021– Published 18 May, 2026
Vol. 1
  • Received 15 January 2026
  • Revised 14 April 2026
  • Accepted 6 May 2026
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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.

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