Thermal brachistochrone for harmonically confined Brownian particles

Abstract

The overdamped Brownian dynamics of a harmonic oscillator is a paradigmatic system in non-equilibrium statistical mechanics, which reliably models relevant stochastic systems such as colloidal particles submitted to optical confinement. In this work, optimal thermal protocols are tailored to minimise the connection time between equilibrium states of overdamped $d$-dimensional oscillators. Application of control theory reveals that these optimal protocols are of bang-bang type, that is, the temperature of the bath has to take alternatively the minimum and maximum values allowed. Minimum connection times increase with the considered dimension $d$. Remarkably, this is the case even for symmetric oscillators, for example, with spherical symmetry -- in which the degeneracy of the elastic constant along the $d$ possible directions seems to imply a minimum connection time equal to that for the one-dimensional case. This surprising unavoidable price to pay when increasing dimension is thoroughly investigated and understood on a physical basis. Moreover, information theory tools such as the thermodynamic length and its divergence are analysed over the brachistochrone.

References in corpus (42)

• 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
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Brownian Carnot engine
• Measuring thermodynamic length
• Irreversible entropy production, from quantum to classical
• Optimal finite-time processes in stochastic thermodynamics
• Thermodynamic metrics and optimal paths
• Speed Limit for Classical Stochastic Processes
• A Micrometer-sized Heat Engine Operating Between Bacterial Reservoirs
• Optimal protocols and optimal transport in stochastic thermodynamics
• Engineered swift equilibration of a Brownian particle
• Boosting work characteristics and overall heat engine performance via shortcuts to adiabaticity: quantum and classical systems
• Stochastic thermodynamic interpretation of information geometry
• Time-information uncertainty relations in thermodynamics
• Adiabatic processes realized with a trapped Brownian particle
• Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
• Shortcuts to isothermality and nonequilibrium work relations
• Shortcut-to-adiabaticity Otto engine: A twist to finite-time thermodynamics
• Shortcuts to adiabaticity using flow fields
• Exact non-equilibrium solutions of the Boltzmann equation under a time-dependent external force
• Shortcuts to Adiabatic Pumping in Classical Stochastic Systems
• Thermal bath Engineering for Swift Equilibration
• Boundary layers in stochastic thermodynamics
• Nonequilibrium uncertainty principle from information geometry
• Fast forward approach to stochastic heat engine
• Finite-time adiabatic processes: derivation and speed limit
• Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator
• Optimising the relaxation route with optimal control
• Abstract models for heat engines
• Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap
• 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
• On extremals of the entropy production by "Langevin-Kramers" dynamics
• On the efficiency of heat engines at the micro-scale and below
• An application of Pontryagin's principle to Brownian particle engineered equilibration
• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• Speed limit for open systems coupled to general environments
• Optimization of stochastic thermodynamic machines
• Optimal control of uniformly heated granular fluids in linear response

Cited by in corpus (12)

• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Heating and Cooling are Fundamentally Asymmetric and Evolve Along Distinct Pathways
• Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects
• Optimal time-entropy bounds and speed limits for Brownian thermal shortcuts
• Non-equilibrium memory effects: granular fluids and beyond
• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Optimal control of levitated nanoparticles through finite-stiffness confinement
• Optimal synchronisation to a limit cycle
• Active charge and discharge of a capacitor: scaling solution and energy optimization
• Maximum power Stirling-like heat engine with a harmonically confined Brownian particle
• Time-optimal synchronisation to self-sustained oscillations under bounded control