Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
arXiv:1412.5138 · doi:10.1103/PhysRevE.91.042114
Abstract
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non- Markovian nature of the dynamics requires a modification of the basic relation between dissipation and time-reversal symmetry breaking. The new relation includes a contribution arising from the acausal character of the reverse process. This in turn leads to another second-law-like inequality. We illustrate the general formalism by a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
arXiv comment35 pages, 20 figures. A few misprints corrected and cosmetic changes in the figures. To appear in Phys. Rev. E
References in corpus (74)
- Measuring Information Transfer
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Entropy production along a stochastic trajectory and an integral fluctuation theorem
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Fluctuation theorem for stochastic dynamics
- Information heat engine: converting information to energy by feedback control
- Path ensembles averages in systems driven far-from-equilibrium
- The Physics of Maxwell's demon and information
- Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
- Generalized Jarzynski Equality under Nonequilibrium Feedback Control
- Dissipation: The phase-space perspective
- Second Law of Thermodynamics with Discrete Quantum Feedback Control
- Mechanical systems in the quantum regime
- Stochastic thermodynamics under coarse-graining
- Feedback cooling of a cantilever's fundamental mode below 5 mK
- Noise-induced dynamics in bistable systems with delay
- Work and information processing in a solvable model of Maxwell's demon
- Experimental study of mutual information in a Maxwell Demon
- Nonequilibrium Thermodynamics of Feedback Control
- Thermodynamics of a physical model implementing a Maxwell demon
- Thermodynamics with continuous information flow
- The Three Faces of the Second Law: II. Fokker-Planck Formulation
- Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
- Path-integral analysis of fluctuation theorems for general Langevin processes
- Information-theoretic approach to the study of control systems
- Mutual information between in- and output trajectories of biochemical networks
- Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell's demon interpretation
- Thermodynamics of feedback controlled systems
- Information Thermodynamics on Causal Networks
- Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems
- Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
- Maxwell's Refrigerator: An Exactly Solvable Model
- Lower bounds on dissipation upon coarse graining
- Second-law-like inequalities with information and their interpretations
- Unifying Three Perspectives on Information Processing in Stochastic Thermodynamics
- Non-equilibrium and information: the role of cross-correlations
- Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
- Thermodynamics of genuine non-equilibrium states under feedback control
- Realization of a feedback controlled flashing ratchet
- Cooling and control of a cavity opto-electromechanical system
- Generalized detailed Fluctuation Theorem under Nonequilibrium Feedback control
- Symmetries of generating functionals of Langevin processes with colored multiplicative noise
- Thermodynamic efficiency of information and heat flow
- Steady state fluctuation relations for systems driven by an external random force
- Fluctuation Theorems of Brownian Particles Controlled by a Maxwell's Demon
- Non-equilibrium work fluctuations for oscillators in non-Markovian baths
- Fluctuation relations and coarse-graining
- Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
- Full mechanical characterization of a cold damped mirror
- Entropy Production of Brownian Macromolecules with Inertia
- Fluctuation theorems for harmonic oscillators
- Feedback cooling of the normal modes of a massive electromechanical system to submillikelvin temperature
- Fluctuation relations for a driven Brownian particle
- Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control
- Continuous time random walk for open systems: Fluctuation theorems and counting statistics
- Time-Delayed Feedback control of a flashing ratchet
- Harmonic Oscillator in Heat Bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark statistics
- Effect of time delay on feedback control of a flashing ratchet
- Fluctuation theorems in presence of information gain and feedback
- An illustrative example of the relationship between dissipation and relative entropy
- Current fluctuations in stochastic systems with long-range memory
- Dynamical fluctuations for semi-Markov processes
- Fluctuation relations for anomalous dynamics
- Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited
- Maximum work extraction and implementation costs for non-equilibrium Maxwell's demons
- Mutual Entropy-Production and Sensing in Bipartite Systems
- Delay-induced transport in a rocking ratchet under feedback control
- Information Anatomy of Stochastic Equilibria
- Fluctuation relations for driven coupled classical two-level systems
- Finite-time thermodynamics of port-Hamiltonian systems
- Transport reversal in a delayed feedback ratchet
- Non-adiabatic entropy production for non-Markov dynamics
- Feedback cooling of cantilever motion using a quantum point contact transducer
Cited by in corpus (35)
- Irreversibility, heat and information flows induced by non-reciprocal interactions
- Levitated Nanoparticles for Microscopic Thermodynamics - A Review
- Sensory capacity: an information theoretical measure of the performance of a sensor
- Thermodynamics of continuous non-Markovian feedback control
- Heat flow due to time-delayed feedback
- Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations
- Stochastic thermodynamics of relativistic Brownian motion
- Thermodynamic uncertainty relation for time-delayed Langevin systems
- Multimode cold-damping optomechanics with delayed feedback
- Uncertainty relations for time-delayed Langevin systems
- Brownian Molecules Formed by Delayed Harmonic Interactions
- Stochastic thermodynamics with arbitrary interventions
- Force-linearization closure for non-Markovian Langevin systems with time delay
- Fokker-Planck equations for time-delayed systems via Markovian Embedding
- All electrical cooling of an optically levitated nanoparticle
- Heat fluctuations for underdamped Langevin dynamics
- Information thermodynamics for a multi-feedback process with time delay
- Thermodynamics of collective enhancement of precision
- Laminar Chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of Laminar Chaos
- Nonequilibrium steady states in Langevin thermal systems
- Two coupled, driven Ising spin systems working as an Engine
- Equilibrium Stochastic Delay Processes
- Non-reciprocal hidden degrees of freedom: A unifying perspective on memory, feedback, and activity
- Heat production in a stochastic system with nonlinear time-delayed feedback
- Mutual information change in feedback processes driven by measurement
- White-noise fluctuation theorem for Langevin dynamics
- Geometric view of stochastic thermodynamics for non-equilibrium steady states
- Inference of Time-Reversal Asymmetry from Time Series in a Piezoelectric Energy Harvester
- Virtual potential created by a feedback loop: taming the feedback demon to explore stochastic thermodynamics of underdamped systems
- Active energy harvesting and work transduction by hair-cell bundles in bullfrog's inner ear
- Non-Markovian feedback control and acausality: an experimental study
- Characteristic oscillations in frequency-resolved heat dissipation of linear time-delayed Langevin systems: Approach from the violation of the fluctuation-response relation
- Virtual double-well potential for an underdamped oscillator created by a feedback loop
- Delay Feedback Control for Switching Diffusion Systems Based on Discrete Time Observations