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arXiv · 2302.02930

Cost of diffusion: nonlinearity and giant fluctuations

Satya N. Majumdar·Francesco Mori·Pierpaolo Vivo
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Abstract

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 travelled. 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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Satya N. Majumdar, Francesco Mori, Pierpaolo Vivo. 2023-06-13. Cost of diffusion: nonlinearity and giant fluctuations. https://doi.org/10.1103/physrevlett.130.237102

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