Optimal control of uniformly heated granular fluids in linear response
arXiv:2112.02652 · doi:10.3390/e24010131
Abstract
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.
arXiv comment19 pages, 13 figures
References in corpus (49)
- Shortcuts to adiabaticity: concepts, methods, and applications
- Fast optimal frictionless atom cooling in harmonic traps
- Shortcut to adiabatic passage in two and three level atoms
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Brownian Carnot engine
- Optimal finite-time processes in stochastic thermodynamics
- Anomalous cooling and heating - the Mpemba effect and its inverse
- Optimal protocols and optimal transport in stochastic thermodynamics
- When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids
- Exponentially faster cooling in a colloidal system
- Computer simulation of uniformly heated granular fluids
- Randomly Driven Granular Fluids: large scale structure
- Engineered swift equilibration of a Brownian particle
- The Brownian gyrator: a minimal heat engine on the nano-scale
- Randomly Driven Granular Fluids: collisional statistics and short scale structure
- The Mpemba effect in spin glasses is a persistent memory effect
- Exact Hydrodynamic Description of Active Lattice Gases
- Experimental Realization of a Minimal Microscopic Heat Engine
- Faster uphill relaxation in thermodynamically equidistant temperature quenches
- Pre-Cooling Strategy Allows Exponentially Faster Heating
- Shortcuts to isothermality and nonequilibrium work relations
- Translations and Rotations are correlated in Granular Gases
- Electrical Autonomous Brownian Gyrator
- A dissipation bound for thermodynamic control
- Kovacs-like memory effect in driven granular gases
- Thermodynamic uncertainty relations under arbitrary control protocols
- Mpemba effect in molecular gases under nonlinear drag
- Thermal bath Engineering for Swift Equilibration
- Optimal work in a harmonic trap with bounded stiffness
- Transport coefficients of a granular gas of inelastic rough hard spheres
- Universal reference state in a driven homogeneous granular gas
- Role of roughness on the hydrodynamic homogeneous base state of inelastic spheres
- Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
- Engineered Swift Equilibration of a Brownian Gyrator
- Engineered Swift Equilibration for Brownian objects: from underdamped to overdamped dynamics
- Finite-time adiabatic processes: derivation and speed limit
- Scaling and universality of critical fluctuations in granular gases
- Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator
- Steady state representation of the homogeneous cooling state of a granular gas
- Optimising the relaxation route with optimal control
- Fluctuating hydrodynamics for driven granular gases
- Memory effect in uniformly heated granular gases
- Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
- Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force
- Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap
- An application of Pontryagin's principle to Brownian particle engineered equilibration
- Energy fluctuations in a randomly driven granular fluid
- Linear response in the uniformly heated granular gas
- Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles
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- Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
- Thermal brachistochrone for harmonically confined Brownian particles
- Non-equilibrium memory effects: granular fluids and beyond
- Optimal Control in Soft and Active Matter
- Shortcuts To Adiabaticity for Lévy processes in harmonic traps
- Minimum time connection between non-equilibrium steady states: the Brownian gyrator
- Optimal control of levitated nanoparticles through finite-stiffness confinement
- Control protocols for harmonically confined run-and-tumble particles