Cost of Diffusion: Nonlinearity and Giant Fluctuations
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The model-inspired by the way taxi meters work-exhibits a very...
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Veröffentlicht in: | Physical review letters 2023-06, Vol.130 (23), p.237102-237102, Article 237102 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The model-inspired by the way taxi meters work-exhibits a very rich behavior. The cost for trajectories of equal length and equal duration exhibits giant fluctuations at a critical value of the scaled distance traveled. Furthermore, the full distribution of the cost until the target is reached exhibits an interesting "freezing" transition in the large-deviation regime. All the analytical results are corroborated by numerical simulations. Our results also apply to elastic systems near the depinning transition, when driven by a random force. |
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ISSN: | 0031-9007 1079-7114 |
DOI: | 10.1103/PhysRevLett.130.237102 |