Equilibrium free-energy differences from a linear nonequilibrium equality

Li, Geng; Tu, Z. C.

doi:10.1103/physreve.103.032146

Cited by 12 publications

(7 citation statements)

References 44 publications

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“…A. Heat engines SST have been employed in the last decade to design irreversible heat-engines [27,56,71,76,80,82,101,[153][154][155][156][157][158][159][160][161][162][163][164][165][166]. Loosely speaking, these heat engines can be considered as the mesoscopic counterparts of the classical, macroscopic, heat engines, in which the branches of the corresponding cycle last for a finite time.…”

Section: Applications: Heat Engines and Beyondmentioning

confidence: 99%

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Guéry-Odelin¹,

Jarzynski²,

Plata³

et al. 2022

Preprint

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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 finitetime 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 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. Contents 1. Langevin and Fokker-Planck descriptions 2. Stochastic thermodynamics C. Conditions for the existence of Boltzmann's breathers under static confinement D. Derivation of the expression for the minimum irreversible work E. Comparison of speed limit inequalities for the harmonic case

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Section: Applications: Heat Engines and Beyondmentioning

confidence: 99%

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Guéry-Odelin¹,

Jarzynski²,

Plata³

et al. 2022

Preprint

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“…The Brownian particle is coupled to a heat bath with constant temperature T . To realize finite-time isothermal transitions between two equilibrium states with same temperature, Li et al [34,35] proposed a framework of shortcuts to isothermality by introducing an auxiliary potential U a (x, p, t) so that the distribution function of the system always maintains the following canonical form ρ = e βF (λ)−βHo(x,p,λ) ,…”

Section: A Shortcuts To Isothermalitymentioning

confidence: 99%

“…Their approach consists of two steps: determining the driving potential in an extremely slow time evolution and then rescaling the time variable so that the Kramers equation works for finite-time regions. A more straightforward approach is the shortcut to isothermality [34,35] which is the correspondence of quasi-static isothermal process in finite-time thermodynamics. The calculations of work and heat are tractable in shortcuts to isothermality.…”

Section: Introductionmentioning

confidence: 99%

Microscopic low-dissipation heat engine via shortcuts to adiabaticity and shortcuts to isothermality

Zhao¹,

Gong²,

Tu³

2022

Preprint

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We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical expression of the efficiency at maximum power for this kind of engines. This expression satisfies the universal law of efficiency at maximum power up to the second order of the Carnot efficiency. We also analyze the issue of power at any given efficiency for general lowdissipation engines, and then obtain the supremum of the power in three limiting cases respectively.

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“…( 19) represents an ensemble average over trajectories starting from an arbitrary initial distribution ρ(Γ, 0), but with driving protocols designed according to the strategy of shortcuts to isothermality. The third relation establishes an equality between the free energy difference and the mean work performed by the original Hamiltonian H o [34,93],…”

mentioning

confidence: 99%

Nonequilibrium work relations meet engineered thermodynamic control: A perspective for nonequilibrium measurements

2023

EPL

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Nonequilibrium work relations establish a fundamental connection between the equilibrium properties of a system and the ﬂuctuation of work performed during nonequilibrium driving processes. However, high dissipation in fast driving processes often impedes the convergence of these work relations, complicating the accurate measurement and estimation of equilibrium properties. To address this issue, recent advances in the methodology of engineered thermodynamic control have been introduced. The goal of this method is to improve the eﬃciency of nonequilibrium measurements by engineering the driving strategies for the system. The engineered strategies enable the system to follow a desired evolution, thereby enhancing the estimation of equilibrium properties in ﬁnite-rate driving processes. In this perspective, we shed light on recent developments in this ﬁeld. Diﬀerent principles have been reviewed for engineering thermodynamic driving strategies, such as ﬁnding optimal control protocols to minimize dissipation and designing thermodynamic control protocols to shorten the lag between the system current state and its corresponding equilibrium state. Nonequilibrium measurement schemes matched with engineered thermodynamic control are also outlined as promising avenues for improving the eﬃciency and accuracy of nonequilibrium measurements, including several reﬁned nonequilibrium work relations matched with designed thermodynamic control protocols.

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Equilibrium free-energy differences from a linear nonequilibrium equality

Cited by 12 publications

References 44 publications

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Microscopic low-dissipation heat engine via shortcuts to adiabaticity and shortcuts to isothermality

Nonequilibrium work relations meet engineered thermodynamic control: A perspective for nonequilibrium measurements

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