A geometric bound on the efficiency of irreversible thermodynamic cycles

Frim, Adam G.; DeWeese, Michael R.

doi:10.48550/arxiv.2112.10797

Cited by 4 publications

(5 citation statements)

References 56 publications

(103 reference statements)

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“…Mostly, attainingor even exceeding [185]-Carnot's efficiency is connected with the antiadiabatic limit of infinitely fast transformations [159,160,181,183]. Recently, the optimization of quite general heat engines has also been considered [104,186]. In Ref.…”

Section: Applications: Heat Engines and Beyondmentioning

confidence: 99%

“…In Ref. [186], the full space of non-equilibrium thermodynamic cycles is explored but within the linear response regime. Therein, the authors employ information geometry ideas for deriving an upper bound for the efficiency and building finite-time heat engines that outperformin terms of efficiency-other recent proposals.…”

Section: Applications: Heat Engines and Beyondmentioning

confidence: 99%

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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%

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

View full text Add to dashboard Cite

show abstract

“…This has enabled finding optimal driving protocols in such regime for complex systems such as a two dimensional Ising model [33,34], nanomagnets [35], and quantum spin chains [36]. Optimal protocols for different classes of slowly driven heat engines have also been developed by such a geometric approach [32,[37][38][39][40][41][42][43][44]. Besides the slow driving regime, the optimization problem can also be simplified in the opposite, fast-driving, regime [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

et al. 2022

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We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial.

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“…The geometric approach has lead to notable insights on the principles that govern the performance of adiabatic thermal machines [42][43][44][45][46][47][48][49][50]. Recent results include explicit optimization schemes for different types of devices [51][52][53][54][55][56] as well as geometric trade-off relations between the efficiency, power yield [45] and power fluctuations [47] of cyclic heat engines that are driven by continuous temperature variations.…”

mentioning

confidence: 99%

Geometric Bounds on the Power of Adiabatic Thermal Machines

Eglinton,

Brandner

2022

Preprint

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We analyze the performance of slowly driven meso-and micro-scale refrigerators and heat engines that operate between two thermal baths with small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat-leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasi-static limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.

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A geometric bound on the efficiency of irreversible thermodynamic cycles

Cited by 4 publications

References 56 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

Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

Geometric Bounds on the Power of Adiabatic Thermal Machines

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