The geometry of thermodynamic control

Abstract

A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold, and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory.

References in corpus (37)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Brownian motors: noisy transport far from equilibrium
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Information heat engine: converting information to energy by feedback control
• Steady State Thermodynamics of Langevin Systems
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Measuring thermodynamic length
• Optimal finite-time processes in stochastic thermodynamics
• Thermodynamic metrics and optimal paths
• Nonequilibrium Thermodynamics of Feedback Control
• The thermodynamics of prediction
• Nonequilibrium fluctuations in a resistor
• The Energetic Costs of Cellular Computation
• Optimal protocols and optimal transport in stochastic thermodynamics
• An experimental test of the Jarzynski equality in a mechanical experiment
• Refined Second Law of Thermodynamics for fast random processes
• Dissipation and lag in irreversible processes
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Thermodynamic curvature measures interactions
• Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
• Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
• Fluctuations in out of equilibrium systems: from theory to experiment
• Microscopic analysis of Clausius-Duhem processes
• Finite time thermodynamics for a single level quantum dot
• Memory erasure in small systems
• Information geometry in vapour-liquid equilibrium
• Finite-time erasing of information stored in fermionic bits
• Computing the optimal protocol for finite-time processes in stochastic thermodynamics
• Virtual potentials for feedback traps
• Near-equilibrium measurements of nonequilibrium free energy
• Optimal control of transitions between nonequilibrium steady states
• Exactly solvable model illustrating far-from-equilibrium predictions
• Stochastic Optimal Control as Non-equilibrium Statistical Mechanics: Calculus of Variations over Density and Current
• Dissipationless Information Erasure and Landauer's Principle

Cited by in corpus (96)

• Theory of nonequilibrium free energy transduction by molecular machines
• Thermodynamic Geometry of Microscopic Heat Engines
• Thermodynamic length in open quantum systems
• Optimal finite-time erasure of a classical bit
• Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states
• Optimal driving of isothermal processes close to equilibrium
• Geometric optimisation of quantum thermodynamic processes
• A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems
• Dynamic Riemannian Geometry of the Ising Model
• Analysis of slow transitions between nonequilibrium steady states
• A dissipation bound for thermodynamic control
• Action quantum speed limits
• Thermodynamic control -- an old paradigm with new applications
• Contact Symmetries and Hamiltonian Thermodynamics
• Optimal Control in Stochastic Thermodynamics
• Optimal Control of Overdamped Systems
• Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines
• Phase transition in protocols minimizing work fluctuations
• Near-optimal protocols in complex nonequilibrium transformations
• Thermodynamic geometry of minimum-dissipation driven barrier crossing
• Optimal protocols for slowly-driven quantum processes
• Active matter under control: Insights from response theory
• A geometric bound on the efficiency of irreversible thermodynamic cycles
• Minimal dissipation in processes far from equilibrium
• Geometry of work fluctuations versus efficiency in microscopic thermal machines
• Optimal control of transitions between nonequilibrium steady states
• Collective advantages in finite-time thermodynamics
• How difficult is it to prepare a quantum state?
• Extracting maximum power from active colloidal heat engines
• Geometric optimization of non-equilibrium adiabatic thermal machines and implementation in a qubit system
• Optimal Efficiency of a Noisy Quantum Heat Engine
• Energetics of active fluctuations in living cells
• Degenerate optimal paths in thermally isolated systems
• Energy and information flows in autonomous systems
• Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems
• Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines
• Minimally dissipative information erasure in a quantum dot via thermodynamic length
• Optimal finite-time Brownian Carnot engine
• Limited-control optimal protocols arbitrarily far from equilibrium
• Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems
• Quantum information geometry of driven CFTs
• Optimal Control of Rotary Motors
• Optimal discrete control: minimizing dissipation in discretely driven nonequilibrium systems
• Finite-time Landauer principle beyond weak coupling
• Driven probe under harmonic confinement in a colloidal bath
• Optimality of non-conservative driving for finite-time processes with discrete states
• Stochastic control in microscopic nonequilibrium systems
• Diffusion in nonuniform temperature and its geometric analog
• Para-Sasakian geometry in thermodynamic fluctuation theory
• Extrapolating the thermodynamic length with finite-time measurements
• Efficient control protocols for an active Ornstein-Uhlenbeck particle
• Thermodynamic Cost for Classical Counterdiabatic Driving
• Information geometry approach to quantum stochastic thermodynamics
• A universal tradeoff between power, precision and speed in physical communication
• Conformal Gauge Transformations in Thermodynamics
• Optimal Control of the F${}_1$-ATPase Molecular Motor
• Negative entropy production rates in Drude-Sommerfeld metals
• Linear Stochastic Thermodynamics
• Performance of optimal linear-response processes in driven Brownian motion far from equilibrium
• Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines
• Engineered swift equilibration for arbitrary geometries
• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• Least Rattling Feedback from Strong Time-scale Separation
• On the use of stochastic differential geometry for non-equilibrium thermodynamics modeling and control
• Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
• Emergent Newtonian dynamics and the geometric origin of mass
• Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines
• Optimal control of dissipation and work fluctuations for rapidly driven systems
• Thermodynamic optimization of a Penrose process: an engineers' approach to black hole thermodynamics
• Toward the design principles of molecular machines
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Optimal control with a strong harmonic trap
• An Exponential Bound in the Quest for Absolute Zero
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Work statistics in slow thermodynamic processes
• Geometric characterization for cyclic heat engines far from equilibrium
• Optimal schedules for annealing algorithms
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Shortcuts to Thermodynamic Computing: The Cost of Fast and Faithful Erasure
• Speed limit, dissipation bound and dissipation-time trade-off in thermal relaxation processes
• Nonequilibrium work energy relation for non-Hamiltonian dynamics
• Hidden energy flows in strongly coupled nonequilibrium systems
• Contact geometry and quantum thermodynamics of nanoscale steady states
• Finite-time bounds on the probabilistic violation of the second law of thermodynamics
• Riemannian Geometry of Optimal Driving and Thermodynamic Length and its Application to Chemical Reaction Networks
• Hamilton-Jacobi approach to thermodynamic transformations
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Multiparameter optimal control of F1-ATPase
• Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales
• Geometric Foundation of Nonequilibrium Transport: A Minkowski Embedding of Markov Dynamics
• A Study of Curvature Theory for Different Symmetry Classes of Hamiltonian
• Geometric Bounds on the Power of Adiabatic Thermal Machines
• Kibble-Zurek scaling from linear response theory
• Optimal finite-time processes in weakly driven overdamped Brownian motion
• Irreversibility as divergence from equilibrium
• Deterministic particle flows for constraining stochastic nonlinear systems