Geodesic Path for the Minimal Energy Cost in Shortcuts to Isothermality

Li, Geng; Chen, Jingfu; Sun, C. P.; Dong, Huafeng

doi:10.1103/physrevlett.128.230603

Cited by 22 publications

(14 citation statements)

References 47 publications

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“…Finally, we point out that geometric thermodynamics is related to several fascinating topics, and has the potential to clarify the geometric properties of these topics. The classical correspondence of the control protocol called shortcuts to adiabatically for the stochastic process [84][85][86][87][88] is related to the geometry of the probability distribution. Remarkably, the link between shortcuts and information geometry has been proposed in Ref.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport

Ito

2023

Info. Geo.

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We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting our recent results on geometrical aspects of entropy production rate in stochastic thermodynamics for the Fokker–Planck equation, we introduce a geometric framework of non-equilibrium thermodynamics in terms of information geometry and optimal transport theory. We show that the proposed geometric framework is useful for obtaining several non-equilibrium thermodynamic relations, such as thermodynamic trade-off relations between the thermodynamic cost and the fluctuation of the observable, optimal protocols for the minimum thermodynamic cost and the decomposition of the entropy production rate for the non-equilibrium system. We clarify several stochastic-thermodynamic links between information geometry and optimal transport theory via the excess entropy production rate based on a relation between the gradient flow expression and information geometry in the space of probability densities and a relation between the velocity field in optimal transport and information geometry in the space of path probability densities.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport

Ito

2023

Info. Geo.

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“…and note that the last term on the right-hand side is of a higher order in τ −1 than the first two, since ġ(t) ∝ τ −1 and g(t) ∝ τ −2 . Hence, as long as the relaxation function Ψ i is composed of sums of oscillatory functions (as in equations ( 32), (38) and (A7)), we can drop the last term, and the same applies to the outer integral in equation (33). If this is done consistently, the LRT excess work reduces to…”

Section: Data Availability Statementmentioning

confidence: 99%

“…To begin, consider first equation (33) for the excess work calculated by means of LRT-it already expresses the leading order of the excess work in Δ when Δ → 0. We want to find its adiabatic limit, that is, the leading order in τ −1 for τ → ∞.…”

Section: Data Availability Statementmentioning

confidence: 99%

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Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems

2022

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The task of finding optimal protocols that minimize the energetic cost of thermodynamic processes of long yet finite duration $\tau$ is a pressing one. We approach this problem here in a rigorous and systematic fashion by means of the adiabatic perturbation theory of closed Hamiltonian quantum systems. Our main finding is a $1/\tau^2$ scaling of the excess work for large $\tau$ in gapped systems. This result is at odds with the asymptotic $1/\tau$ prediction of the geometric approach to optimization, which is predicated on the slow evolution of open systems close to canonical equilibrium. In contrast, our approach does not lead to an obvious geometric interpretation. Furthermore, as the thermodynamic work does not depend on how an isolated quantum system is split into a system of interest and its environment, our results imply the failure of the geometric approach prediction even for open systems. Additionally, we provide alternative optimization procedures, both for slowly-varying processes described by adiabatic perturbation theory and for weakly-varying processes described by linear response theory. Our findings are benchmarked and confirmed through the application to the driven transverse-field Ising chain.

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“…In order to generalise eq. ( 1) to the strong coupling regime, we exploit the framework of thermodynamic geometry [33][34][35][36][37][38][39], which has proven extremely successful to devise minimally dissipative processes both in classical [37,[81][82][83][84][85][86][87] and quantum systems [13,47,[88][89][90][91][92].…”

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confidence: 99%

Finite-time Landauer principle at strong coupling

Alberto¹,

Perarnau-Llobet²

2022

Preprint

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Landauer's principle gives a fundamental limit to the thermodynamic cost of erasing information. Its saturation requires a reversible isothermal process, and hence infinite time. We develop a finitetime version of Landauer's principle for a bit encoded in the occupation of a single fermionic mode, which can be strongly coupled to a reservoir. By solving the exact non-equilibrium dynamics, we optimize erasure processes (taking both the fermion's energy and system-bath coupling as control parameters) in the slow driving regime through a geometric approach to thermodynamics. We find analytic expressions for the thermodynamic metric and geodesic equations, which can be solved numerically. Their solution yields optimal processes that allow us to characterize a finite-time correction to Landauer's bound, fully taking into account non-markovian and strong coupling effects.

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Geodesic Path for the Minimal Energy Cost in Shortcuts to Isothermality

Cited by 22 publications

References 47 publications

Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport

Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport

Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems

Finite-time Landauer principle at strong coupling

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