Cost of diffusion: nonlinearity and giant fluctuations
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.
Keywords
Cite
@article{arxiv.2302.02930,
title = {Cost of diffusion: nonlinearity and giant fluctuations},
author = {Satya N. Majumdar and Francesco Mori and Pierpaolo Vivo},
journal= {arXiv preprint arXiv:2302.02930},
year = {2023}
}
Comments
4 fig. 6 pages + Supplemental Material included. Published version, which includes physical applications to elastic systems in presence of random forces. Title changed to match published version