To reset or not to reset, that is the question!

Stochastic resetting [1], i.e, stopping an ongoing dynamical process to start over, can either accelerate or hinder a first-passage process. Tuning system parameters can invert the effect of resetting on the mean completion time of the process, leading to a resetting transition. In this talk, I shall first explore the exact conditions where stochastic resetting accelerates diffusive transport for a couple of analytically tractable systems, viz.,

(i) diffusion in a linear potential, where the resetting transition is found to be governed by the Péclet number [2],

(ii) diffusion in a logarithmic potential, that exhibits a series of dynamical transitions when the constant strength of the potential in the units of thermal energy, is tuned [3].

Based on the common trends that these model systems show, a general framework can be proposed that reveals that the resetting transition is governed by an interplay between thermal and potential energy; when thermal energy dominates the dynamics, resetting can expedite the process [4]. Finally, considering a toy model for space-dependent diffusion ,I shall show that whenever a dynamical process is diffusion-controlled, resetting can, in principle, accelerate it [5]. We believe that our analysis will be useful in a variety of natural as well as man-made systems where resetting plays a crucial role in diffusive transport.

References:

[1] M. R. Evans, S. N. Majumdar, and G. Schehr, J. Phys. A: Math. Theor. 53, 193001(2020).

[2] S. Ray, D. Mondal and S. Reuveni, J. Phys. A: Math. Theor. 52, 255002 (2019).

[3] S. Rayand S. Reuveni, J. Chem. Phys. 152, 234110, (2020).

[4] S. Rayand S. Reuveni, J. Chem. Phys. (Comm.) 154, 171103, (2021).

[5] S. Ray, J. Chem. Phys. 153, 234904, (2020).

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