Ergodicity Breaking in Active Run-and-Tumble Particles in a Double-Well Potential
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arXiv
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| Format: | Preprint |
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2025
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| author | Basu, Urna Majumdar, Satya N. Rosso, Alberto |
| author_facet | Basu, Urna Majumdar, Satya N. Rosso, Alberto |
| contents | 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 Kramer's-Arrhenius law, and displays a divergence near the critical height following a Vogel-Fulcher-Tammann-like form with an anomalous exponent $1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity Breaking in Active Run-and-Tumble Particles in a Double-Well Potential Basu, Urna Majumdar, Satya N. Rosso, Alberto Statistical Mechanics 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 Kramer's-Arrhenius law, and displays a divergence near the critical height following a Vogel-Fulcher-Tammann-like form with an anomalous exponent $1/2$. |
| title | Ergodicity Breaking in Active Run-and-Tumble Particles in a Double-Well Potential |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.23641 |