Optimal Control of Overdamped Systems

Abstract

Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles underlying biological processes at the molecular level. Recent work has demonstrated that when a thermodynamic system is driven away from equilibrium then the space of controllable parameters has a Riemannian geometry induced by a generalized inverse diffusion tensor. We derive a simple, compact expression for the inverse diffusion tensor that depends solely on equilibrium information for a broad class of potentials. We use this formula to compute the minimal dissipation for two model systems relevant to small-scale information processing and biological molecular motors. In the first model, we optimally erase a single classical bit of information modelled by an overdamped particle in a smooth double-well potential. In the second model, we find the minimal dissipation of a simple molecular motor model coupled to an optical trap. In both models, we find that the minimal dissipation for the optimal protocol is inversely proportional to protocol duration, as expected, though the dissipation for the erasure model takes a different form than what we found previously for a similar system.

References in corpus (10)

• High-precision test of Landauer's principle in a feedback trap
• Optimal finite-time processes in stochastic thermodynamics
• Nonequilibrium fluctuations in a resistor
• Comparison of far-from-equilibrium work relations
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• The geometry of thermodynamic control
• Finite-time erasing of information stored in fermionic bits
• Computing the optimal protocol for finite-time processes in stochastic thermodynamics
• Comparison of work fluctuation relations
• Analysis of slow transitions between nonequilibrium steady states

Cited by in corpus (43)

• Finite-time Landauer principle
• Theory of nonequilibrium free energy transduction by molecular machines
• Thermodynamic length in open quantum systems
• Finite-Time Quantum Landauer Principle and Quantum Coherence
• Geometric optimisation of quantum thermodynamic processes
• Maximum Efficiency of Low-Dissipation Heat Engines at Arbitrary Power
• A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems
• Dynamic Riemannian Geometry of the Ising Model
• Efficiency at and near Maximum Power of Low-Dissipation Heat Engines
• Thermodynamic control -- an old paradigm with new applications
• Optimal finite-time bit erasure under full control
• Optimal Control in Stochastic Thermodynamics
• Near-optimal protocols in complex nonequilibrium transformations
• Thermodynamic geometry of minimum-dissipation driven barrier crossing
• A geometric bound on the efficiency of irreversible thermodynamic cycles
• Minimal dissipation in processes far from equilibrium
• Extracting maximum power from active colloidal heat engines
• Diverging, but negligible power at Carnot efficiency: theory and experiment
• Optimal finite-time Brownian Carnot engine
• Fundamental energy cost of finite-time computing
• Optimal Control of Rotary Motors
• Optimal discrete control: minimizing dissipation in discretely driven nonequilibrium systems
• Driven probe under harmonic confinement in a colloidal bath
• Optimality of non-conservative driving for finite-time processes with discrete states
• Harnessing Fluctuations in Thermodynamic Computing via Time-Reversal Symmetries
• Thermodynamic Computing
• Adiabatic computing for optimal thermodynamic efficiency of information processing
• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• Performance of optimal linear-response processes in driven Brownian motion far from equilibrium
• Engineered swift equilibration for arbitrary geometries
• Refining Landauer's Stack: Balancing Error and Dissipation When Erasing Information
• Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines
• Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics
• Optimal control with a strong harmonic trap
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Reliability and operation cost of underdamped memories during cyclic erasures
• Thermodynamics of majority-logic decoding in information erasure
• Shortcuts to Thermodynamic Computing: The Cost of Fast and Faithful Erasure
• Nonequilibrium work energy relation for non-Hamiltonian dynamics
• Perturbative expansion of irreversible works in symmetric and asymmetric processes
• Global thermodynamic manifold for conservative control of stochastic systems
• Optimal finite-time processes in weakly driven overdamped Brownian motion