Cost of Diffusion: Nonlinearity and Giant Fluctuations

TY - JOUR

T1 - Cost of Diffusion

T2 - Nonlinearity and Giant Fluctuations

AU - Majumdar, Satya N.

AU - Mori, Francesco

AU - Vivo, Pierpaolo

N1 - Funding Information: This work was supported by a Leverhulme Trust International Professorship Grant (No. LIP-2020-014). Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"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.

PY - 2023/6/9

Y1 - 2023/6/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85162753892&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.130.237102

DO - 10.1103/PhysRevLett.130.237102

M3 - Article

C2 - 37354426

AN - SCOPUS:85162753892

SN - 0031-9007

VL - 130

JO - Physical Review Letters

JF - Physical Review Letters

IS - 23

M1 - 237102

ER -