Work statistics at first-passage times
Year: 2024
Type: article
Abstract: We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterised by a first passage event that marks the completion of the non-equilibrium process. In particular, we consider a particle diffusing in one dimension in the presence of a time-dependent potential U ( x , t ) = k | x − v t | n / n , where k > 0 is the stiffness and n > 0 is the order of the potential. Moreover, the particle is confined between two absorbing walls, located at L ± ( t ) , that move with a constant velocity v and are initially located at L ± ( 0 ) = ± L . As soon as the particle reaches any of the boundaries, the process is said to be completed and here, we compute the work done W by the particle in the modulated trap upto this random time. Employing the Feynman–Kac path integral approach, we find that the typical values of the work scale with L with a crucial dependence on the order n . While for n > 1, we show that ⟨ W ⟩ ∼ L 1 − n exp k L n / n − v L / D for large L , we get an algebraic scaling of the form ⟨ W ⟩ ∼ L n for the n < 1 case. The marginal case of n = 1 is exactly solvable and our analysis unravels three distinct scaling behaviours: (i) ⟨ W ⟩ ∼ L for v > k , (ii) ⟨ W
Source: New Journal of Physics
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,485
OpenAlex ID: W4392564737