1
|
Raynal D, de Guillebon T, Guéry-Odelin D, Trizac E, Lauret JS, Rondin L. Shortcuts to Equilibrium with a Levitated Particle in the Underdamped Regime. PHYSICAL REVIEW LETTERS 2023; 131:087101. [PMID: 37683149 DOI: 10.1103/physrevlett.131.087101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 07/24/2023] [Indexed: 09/10/2023]
Abstract
We report on speeding-up equilibrium recovery in the previously unexplored general case of the underdamped regime using an optically levitated particle. We accelerate the convergence toward equilibrium by an order of magnitude compared to the natural relaxation time. We then discuss the efficiency of the studied protocols, especially for a multidimensional system. These results pave the way for optimizing realistic nanomachines with application to sensing and developing efficient nanoheat engines.
Collapse
Affiliation(s)
- Damien Raynal
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| | - Timothée de Guillebon
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| | - David Guéry-Odelin
- Université Paul Sabatier-Toulouse 3, CNRS, LCAR, 31062 Toulouse Cedex 9, France
| | - Emmanuel Trizac
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay Cedex, France
- Univ Lyon, ENS de Lyon, F-69342 Lyon, France
| | - Jean-Sébastien Lauret
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| | - Loïc Rondin
- Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, 91405 Orsay Cedex, France
| |
Collapse
|
2
|
Guéry-Odelin D, Jarzynski C, Plata CA, Prados A, Trizac E. Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:035902. [PMID: 36535018 DOI: 10.1088/1361-6633/acacad] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 12/19/2022] [Indexed: 06/17/2023]
Abstract
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.
Collapse
Affiliation(s)
- David Guéry-Odelin
- Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, CNRS, Toulouse, France
| | - Christopher Jarzynski
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, United States of America
- Institute for Physical Science and Technology, University of Maryland, College Park, MD, United States of America
- Department of Physics, University of Maryland, College Park, MD, United States of America
| | - Carlos A Plata
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | | |
Collapse
|
3
|
Zhong A, DeWeese MR. Limited-control optimal protocols arbitrarily far from equilibrium. Phys Rev E 2022; 106:044135. [PMID: 36397571 DOI: 10.1103/physreve.106.044135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 09/16/2022] [Indexed: 06/16/2023]
Abstract
Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and experimental contexts, systems often may only be controlled with a limited set of degrees of freedom. Here, going beyond slow- and fast-driving approximations employed in previous studies, we obtain exact finite-time optimal protocols for this limited-control setting. By working with deterministic Fokker-Planck probability density time evolution, we can frame the work-minimizing protocol problem in the standard form of an optimal control theory problem. We demonstrate that finding the exact optimal protocol is equivalent to solving a system of Hamiltonian partial differential equations, which in many cases admit efficiently calculable numerical solutions. Within this framework, we reproduce analytical results for the optimal control of harmonic potentials and numerically devise optimal protocols for two anharmonic examples: varying the stiffness of a quartic potential and linearly biasing a double-well potential. We confirm that these optimal protocols outperform other protocols produced through previous methods, in some cases by a substantial amount. We find that for the linearly biased double-well problem, the mean position under the optimal protocol travels at a near-constant velocity. Surprisingly, for a certain timescale and barrier height regime, the optimal protocol is also nonmonotonic in time.
Collapse
Affiliation(s)
- Adrianne Zhong
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA and Redwood Center For Theoretical Neuroscience and Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California 94720, USA
| |
Collapse
|
4
|
Frim AG, DeWeese MR. Optimal finite-time Brownian Carnot engine. Phys Rev E 2022; 105:L052103. [PMID: 35706186 DOI: 10.1103/physreve.105.l052103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 04/29/2022] [Indexed: 06/15/2023]
Abstract
Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional "textbook" engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finite-time nonequilibrium cyclic operation of the parametric harmonic oscillator in contact with a time-varying heat bath with particular focus on the Brownian Carnot cycle. We derive the optimally parametrized Carnot cycle, along with two other new cycles and compare their dissipated energy, efficiency, and steady-state power production against each other and a previously tested experimental protocol for the Carnot cycle. We demonstrate a 20% improvement in dissipated energy over previous experimentally tested protocols and a ∼50% improvement under other conditions for one of our engines, whereas our final engine is more efficient and powerful than the others we considered. Our results provide the means for experimentally realizing optimal mesoscale heat engines.
Collapse
Affiliation(s)
- Adam G Frim
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
- Redwood Center For Theoretical Neuroscience, University of California, Berkeley, Berkeley, California 94720, USA
- Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California 94720, USA
| |
Collapse
|
5
|
Plata CA, Prados A, Trizac E, Guéry-Odelin D. Taming the Time Evolution in Overdamped Systems: Shortcuts Elaborated from Fast-Forward and Time-Reversed Protocols. PHYSICAL REVIEW LETTERS 2021; 127:190605. [PMID: 34797129 DOI: 10.1103/physrevlett.127.190605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Revised: 09/01/2021] [Accepted: 10/06/2021] [Indexed: 06/13/2023]
Abstract
Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution toward a well chosen common intermediate state, we analytically derive a smooth protocol to connect two arbitrary states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current-rather limited-catalog of explicit protocols, but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed.
Collapse
Affiliation(s)
- Carlos A Plata
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | | | - David Guéry-Odelin
- Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, 118 Route de Narbonne, F-31062 Toulouse, France
| |
Collapse
|