2000 character limit reached
Ratchet-mediated resetting: Current, efficiency, and exact solution
Published 17 May 2024 in cond-mat.stat-mech, math-ph, and math.MP | (2405.10698v2)
Abstract: We model an overdamped Brownian particle that is subject to resetting facilitated by a ratchet potential on a spatially periodic domain. This asymmetric potential switches on with a constant rate, but switches off again only upon the particle's first passage to a resetting point at the minimum of the potential. Repeating this cycle sustains a non-equilibrium steady-state, as well as a directed steady-state current which can be harnessed to perform useful work. We derive exact analytic expressions for the probability densities of the free-diffusion and resetting phases, the associated currents for each phase, and an efficiency parameter that quantifies the return in current for given power input. These expressions allow us to fully characterise the system and obtain experimentally relevant results such as the optimal current and efficiency. Our results are corroborated by simulations, and have implications for experimentally viable finite-time resetting protocols.
- M. R. Evans and S. N. Majumdar, Diffusion with Stochastic Resetting, Phys. Rev. Lett. 106, 160601 (2011a).
- M. R. Evans, S. N. Majumdar, and G. Schehr, Stochastic resetting and applications, J. Phys. A: Math. Theor. 53, 193001 (2020).
- S. Gupta and A. M. Jayannavar, Stochastic Resetting: A (Very) Brief Review, Frontiers in Physics 10 (2022).
- M. R. Evans, S. N. Majumdar, and K. Mallick, Optimal diffusive search: Nonequilibrium resetting versus equilibrium dynamics, J. Phys. A: Math. Theor. 46, 185001 (2013).
- A. Pal, A. Kundu, and M. R. Evans, Diffusion under time-dependent resetting, J. Phys. A: Math. Theor. 49, 225001 (2016).
- A. Pal and S. Reuveni, First Passage under Restart, Phys. Rev. Lett. 118, 030603 (2017).
- M. R. Evans and S. N. Majumdar, Diffusion with optimal resetting, J. Phys. A: Math. Theor. 44, 435001 (2011b).
- H. Alston and T. Bertrand, Boosting macroscopic diffusion with local resetting (2024), arxiv:2401.12772 [cond-mat, physics:physics] .
- D. Boyer and C. Solis-Salas, Random Walks with Preferential Relocations to Places Visited in the Past and their Application to Biology, Phys. Rev. Lett. 112, 240601 (2014).
- M. L. Ginsberg, Dynamic Backtracking, The Journal of Artificial Intelligence Research 1, 25 (1993).
- W.-Y. Cheng and S. Zhang, The Analytics of Reset Options, The Journal of Derivatives 8, 59 (2000).
- S. Lahiri and S. Gupta, Efficiency of a microscopic heat engine subjected to stochastic resetting, Phys. Rev. E 109, 014129 (2024).
- H. Alston, L. Cocconi, and T. Bertrand, Non-equilibrium thermodynamics of diffusion in fluctuating potentials, J. Phys. A: Math. Theor. 55, 274004 (2022).
- A. Pal, Ł. Kuśmierz, and S. Reuveni, Invariants of motion with stochastic resetting and space-time coupled returns, New J. Phys. 21, 113024 (2019a).
- A. Pal, Ł. Kuśmierz, and S. Reuveni, Search with home returns provides advantage under high uncertainty, Phys. Rev. Res. 2, 043174 (2020).
- A. S. Bodrova and I. M. Sokolov, Resetting processes with noninstantaneous return, Phys. Rev. E 101, 052130 (2020a).
- A. Pal, Ł. Kuśmierz, and S. Reuveni, Time-dependent density of diffusion with stochastic resetting is invariant to return speed, Phys. Rev. E 100, 040101 (2019b).
- A. Masó-Puigdellosas, D. Campos, and V. Méndez, Transport properties of random walks under stochastic noninstantaneous resetting, Phys. Rev. E 100, 042104 (2019).
- A. S. Bodrova and I. M. Sokolov, Brownian motion under noninstantaneous resetting in higher dimensions, Phys. Rev. E 102, 032129 (2020b).
- G. Mercado-Vásquez, D. Boyer, and S. N. Majumdar, Reducing mean first passage times with intermittent confining potentials: A realization of resetting processes, J. Stat. Mech. 2022, 093202 (2022).
- I. Santra, S. Das, and S. K. Nath, Brownian motion under intermittent harmonic potentials, J. Phys. A: Math. Theor. 54, 334001 (2021).
- D. Gupta, A. Pal, and A. Kundu, Resetting with stochastic return through linear confining potential, J. Stat. Mech. 2021, 043202 (2021).
- A. Biswas, A. Kundu, and A. Pal, Stochasticity in returns can expedite classical first passage under resetting (2023), arxiv:2307.16294 [cond-mat] .
- J. Fuchs, S. Goldt, and U. Seifert, Stochastic thermodynamics of resetting, EPL 113, 60009 (2016).
- D. Gupta and C. A. Plata, Work fluctuations for diffusion dynamics submitted to stochastic return, New J. Phys. 24, 113034 (2022).
- D. Gupta, C. A. Plata, and A. Pal, Work Fluctuations and Jarzynski Equality in Stochastic Resetting, Phys. Rev. Lett. 124, 110608 (2020b).
- D. M. Busiello, D. Gupta, and A. Maritan, Entropy production in systems with unidirectional transitions, Phys. Rev. Research 2, 023011 (2020).
- F. Jülicher, A. Ajdari, and J. Prost, Modeling molecular motors, Rev. Mod. Phys. 69, 1269 (1997).
- R. D. Astumian and P. Hänggi, Brownian Motors, Physics Today 55, 33 (2002).
- M. Schliwa and G. Woehlke, Molecular motors, Nature 422, 759 (2003).
- M. O. Magnasco, Forced thermal ratchets, Phys. Rev. Lett. 71, 1477 (1993).
- R. D. Astumian and M. Bier, Fluctuation driven ratchets: Molecular motors, Phys. Rev. Lett. 72, 1766 (1994).
- C. R. Doering, Randomly rattled ratchets, Il Nuovo Cimento D 17, 685 (1995).
- L. Angelani, A. Costanzo, and R. Di Leonardo, Active ratchets, EPL 96, 68002 (2011).
- Z. Zhen and G. Pruessner, Optimal Ratchet Potentials for Run-and-Tumble particles (2022), arxiv:2204.04070 [cond-mat] .
- M. Su and B. Lindner, Active Brownian particles in a biased periodic potential, Eur. Phys. J. E 46, 22 (2023).
- N. Razin, Entropy production of an active particle in a box, Phys. Rev. E 102, 030103 (2020).
- R. Garcia-Millan and G. Pruessner, Run-and-tumble motion in a harmonic potential: Field theory and entropy production, J. Stat. Mech. 2021, 063203 (2021).
- M. Caraglio and T. Franosch, Analytic Solution of an Active Brownian Particle in a Harmonic Well, Phys. Rev. Lett. 129, 158001 (2022).
- C. Roberts and G. Pruessner, Exact solution of a boundary tumbling particle system in one dimension, Phys. Rev. Research 4, 033234 (2022).
- Y. Fang, Y. Tian, and C. Zeng, Stochastic resetting-induced reentrance phenomena of inertial Brownian particle in the rough periodic potential, Eur. Phys. J. Plus 138, 808 (2023).
- L. Cocconi, J. Knight, and C. Roberts, Optimal Power Extraction from Active Particles with Hidden States, Phys. Rev. Lett. 131, 188301 (2023).
- L. Cocconi and L. Chen, On the efficiency of an autonomous dynamic Szilard engine operating on a single active particle (2024), arxiv:2401.08496 [cond-mat, physics:math-ph] .
- J.-F. Derivaux, R. L. Jack, and M. E. Cates, Active–passive mixtures with bulk loading: A minimal active engine in one dimension, J. Stat. Mech. 2023, 083212 (2023).
- A. Pal, S. Reuveni, and S. Rahav, Thermodynamic uncertainty relation for systems with unidirectional transitions, Phys. Rev. Research 3, 013273 (2021).
- P. C. Bressloff, Entropy production for diffusion processes across a semipermeable interface (2024), arxiv:2402.16403 [cond-mat, q-bio] .
- F. Mori, K. S. Olsen, and S. Krishnamurthy, Entropy production of resetting processes, Phys. Rev. Res. 5, 023103 (2023).
- B. De Bruyne and F. Mori, Resetting in stochastic optimal control, Phys. Rev. Research 5, 013122 (2023).
- N. G. Van Kampen, Stochastic processes in physics and chemistry, 3rd ed. (Elsevier North Holland, Amsterdam, 2007).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.