Engineered swift equilibration of a Brownian gyrator

Baldassarri, Andrea; Puglisi, Andrea; Sesta, Luca

doi:10.1103/physreve.102.030105

Cited by 34 publications

(31 citation statements)

References 26 publications

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“…We observe how the times given by Eqs. ( 30) and (37), as well as their approximations (41), rapidly converge to Eq. ( 40) as the bounds separate from unity.…”

Section: Validity Of the Linear Response Approximationmentioning

confidence: 88%

“…Therein, we show the linear response expressions Eq. ( 30) (CH case) and (37) (HC case), together with the approximate linear expression (41), and the non-linear expression (40) for a fullstrength thermostat. We observe how the times given by Eqs.…”

Section: Validity Of the Linear Response Approximationmentioning

confidence: 99%

“…Although the initial and final states are also NESSs in that case, the PDF is Gaussian for all times and the evolution equations for the relevant moments can be exactly solved. Thus, the control problem of this system is simpler, although only non-optimal connections have been worked out, to the best of our knowledge [41].…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of uniformly heated granular fluids in linear response

Ruiz-Pino,

Prados

2021

Preprint

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We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature, by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously-from a mathematical point of view-prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.

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“…We observe how the times given by Eqs. ( 30) and (37), as well as their approximations (41), rapidly converge to Eq. ( 40) as the bounds separate from unity.…”

Section: Validity Of the Linear Response Approximationmentioning

confidence: 88%

Section: Validity Of the Linear Response Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Optimal control of uniformly heated granular fluids in linear response

Ruiz-Pino,

Prados

2021

Preprint

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show abstract

“…Although the initial and final states are also NESSs in that case, the PDF is Gaussian for all times, and the evolution equations for the relevant moments can be exactly solved. Thus, the control problem of this system is simpler, although only non-optimal connections have been worked out, to the best of our knowledge [ 45 ].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

Ruiz-Pino

Prados

2022

Entropy

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We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously—from a mathematical point of view—prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.

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“…In doing so, the system can be brought from a chosen state ρ i (x) to another chosen state ρ f (x), in an arbitrary time. Both states can be equilibrium or, more generally, out-of-equilibrium [38,39].…”

mentioning

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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Engineered swift equilibration of a Brownian gyrator

Cited by 34 publications

References 26 publications

Optimal control of uniformly heated granular fluids in linear response

Optimal control of uniformly heated granular fluids in linear response

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

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

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