Minimal-work principle and its limits for classical systems

Allahverdyan, Armen E.; Nieuwenhuizen, Th. M.

doi:10.1103/physreve.75.051124

Cited by 24 publications

(32 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…González-Resines et al (2017) provide invariant-based STA protocols for the motion of the trolley in a transport operation or for hoisting that guarantee final adiabatic energies for the load. Furthermore these energies are shown to be minimal when averaging over a microcanonical ensemble of initial conditions, consistently with the minimal work principle (Allahverdyan andNieuwenhuizen, 2005, 2007). Indeed the possibility to design robust operations with respect to different perturbations or errors (such as dispersion in the initial conditions, or in cable lengths) and STA&OCT combinations to limit, for example, on-route pendulations, offer a great potential.…”

Section: Cranessupporting

confidence: 60%

Shortcuts to adiabaticity: Concepts, methods, and applications

et al. 2019

View full text Add to dashboard Cite

Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different systems and conditions. A motivation to apply STA methods to quantum systems is to manipulate them on timescales shorter than decoherence times. Thus shortcuts to adiabaticity have become instrumental in preparing and driving internal and motional states in atomic, molecular, and solid-state physics. Applications range from information transfer and processing based on gates or analog paradigms, to interferometry and metrology. The multiplicity of STA paths for the controlling parameters may be used to enhance robustness versus noise and perturbations, or to optimize relevant variables. Since adiabaticity is a widespread phenomenon, STA methods also extended beyond the quantum world, to optical devices, classical mechanical systems, and statistical physics. Shortcuts to adiabaticity combine well with other concepts and techniques, in particular with optimal control theory, and pose fundamental scientific and engineering questions such as finding speed limits, quantifying the third law, or determining process energy costs and efficiencies. We review concepts, methods and applications of shortcuts to adiabaticity and outline promising prospects, as well as open questions and challenges ahead.

show abstract

Section: Cranessupporting

confidence: 60%

Shortcuts to adiabaticity: Concepts, methods, and applications

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Indeed, it can be verified (see Appendix B) that they are the first terms of the series expansion of the quasistatic work for δλ/λ 0 ≪ 1. The last term clearly depends on g(t) and therefore represents the excess work [29,33,34]. Since Ψ 0 (−t) = Ψ 0 (t) [see Eq.…”

Section: Thermally Isolated Systems and The Excess Workmentioning

confidence: 99%

Degenerate optimal paths in thermally isolated systems

Acconcia

Bonança

2015

Phys. Rev. E

View full text Add to dashboard Cite

We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.

show abstract

“…A brief history of the principle and its various formulations and derivations for specific systems and conditions is provided in Refs. [47,48]. For the present context, we shall prove it in Appendix A, considering a microcanonical ensemble of initial conditions of the payload, by generalizing the results in Ref.…”

Section: Invariants and Cranesmentioning

confidence: 57%

Invariant-Based Inverse Engineering of Crane Control Parameters

et al. 2017

View full text Add to dashboard Cite

By applying invariant-based inverse engineering in the small-oscillation regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length) to transport a load between two positions at different heights with minimal final-energy excitation for a microcanonical ensemble of initial conditions. The analogy between ion transport in multisegmented traps or neutral-atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.

show abstract

Minimal-work principle and its limits for classical systems

Cited by 24 publications

References 31 publications

Shortcuts to adiabaticity: Concepts, methods, and applications

Shortcuts to adiabaticity: Concepts, methods, and applications

Degenerate optimal paths in thermally isolated systems

Invariant-Based Inverse Engineering of Crane Control Parameters

Contact Info

Product

Resources

About