Optimization of Stochastic Thermodynamic Machines

Zhang, Yunxin

doi:10.1007/s10955-020-02508-0

Cited by 24 publications

(49 citation statements)

References 48 publications

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“…Entropy production, which characterizes the degree of irreversibility (or dissipation), plays a key role in nonequilibrium stochastic thermodynamics [1][2][3][4]. In recent decades, many studies have been devoted to optimize the performance of stochastic thermodynamic machines, usually by reducing the total entropy production [5][6][7][8][9][10][11][12][13][14][15][16]. A general relation between nonequilibrium currents and entropy production, the thermodynamic uncertainty relation (TUR), is discovered and serves as a fundamental principle of nonequilibrium thermodynamics [17][18][19][20][21][22][23][24][25][26][27][28][29][30], which dictates that the precision of a nonequilibrium time-integrated current observable J is bounded from below by the inverse of the total entropy production (EP) σ, ( J 2 − J 2 )/ J 2 ≥ 2/ σ , with • the average of random variables.…”

Section: Introductionmentioning

confidence: 99%

Entropy production related properties of first passage process

Zhang

2021

Preprint

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With nontrivial entropy production, first passage process is one of the most common nonequilibrium process in stochastic thermodynamics. Using one dimensional birth and death precess as a model framework, approximated expressions of mean first passage time (FPT), mean total number of jumps (TNJ), and their coefficients of variation (CV), are obtained for the case far from equilibrium. Consequently, uncertainty relations for FPT and TNJ are presented. Generally, mean FPT decreases exponentially with entropy production, while mean TNJ decreases exponentially first and then tends to a starting site dependent limit. For forward biased process, the CV of TNJ decreases exponentially with entropy production, while that of FPT decreases exponentially first and then tends to a starting site dependent limit. For backward biased process, both CVs of FPT and TNJ tend to one for large absolute values of entropy production. Related properties about the case of equilibrium are also addressed briefly for comparison.

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Section: Introductionmentioning

confidence: 99%

Entropy production related properties of first passage process

Zhang

2021

Preprint

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“…To illustrate the results obtained above, we present an example with explicit solution, see also [12] for more details. For x 0 = 1, duration t = 1, and probabilities ρ 0 (x) = 1/(2 √ x), ρ 1 (x) = 1, the map Γ(x) = √ x, and the optimal potential is as follows,…”

mentioning

confidence: 99%

“…x 0 ] to [0, x 0 ], and satisfies f (Γ(z), t) = f (z, 0), see [12]. The definition of characteristic curve means that f (…”

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confidence: 99%

“…Meanwhile, though this study assumes that variable x lies in interval [0, x 0 ], same results can be obtained for any other types of domain, such as [0, ∞), (−∞, ∞), [a, b] for any a < b, or other domain composing of multiple subintervals. Similar as in [12], the influence of interval scale x 0 can be analyzed by rescaling probability ρ 0/1 (x) into interval [0, 1].…”

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Work needed to drive a thermodynamic system between two distributions

Zhang

2020

EPL

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In this study, the minimum of work needed to drive a thermodynamic system from one initial distribution to another in given time duration is obtained. Equivalently, for given work, the minimum of time duration needed to complete such transition process is obtained. Our results show that, the minimum of work increases with the change of internal energy and friction coefficient, while decreases with the change of entropy and time duration. The results of this study are valuable for the understanding of nonequilibrium thermodynamic, especially for the design and optimization of stochastic heat engines.

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“…(2) Unfortunately, except in a few cases, like that of a Gaussian distribution [12,26], shape preserving evolutions [41], or other very specific situations [33,41], Eq. ( 2) is impractical since it does not lead to an explicit closedform potential U (x, t) [42].…”

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confidence: 99%

Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols

Plata,

Prados,

Trizac

et al. 2021

Preprint

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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 towards a well chosen common intermediate state, we derive analytically 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-catalogue 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.

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Optimization of Stochastic Thermodynamic Machines

Cited by 24 publications

References 48 publications

Entropy production related properties of first passage process

Entropy production related properties of first passage process

Work needed to drive a thermodynamic system between two distributions

Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols

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