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.
35 pages, 20 figures. A few misprints corrected and cosmetic changes in the figures. To appear in Phys. Rev. E
References in corpus (35)
- 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
- Dissipation: The phase-space perspective
- Second Law of Thermodynamics with Discrete Quantum Feedback Control
- Feedback cooling of a cantilever's fundamental mode below 5 mK
- Work and information processing in a solvable model of Maxwell's demon
- Experimental study of mutual information in a Maxwell Demon
- Thermodynamics of a physical model implementing a Maxwell demon
- Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
- Path-integral analysis of fluctuation theorems for general Langevin processes
- Thermodynamics of feedback controlled systems
- Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
- Lower bounds on dissipation upon coarse graining
- Second-law-like inequalities with information and their interpretations
- Realization of a feedback controlled flashing ratchet
- Symmetries of generating functionals of Langevin processes with colored multiplicative noise
- Non-equilibrium work fluctuations for oscillators in non-Markovian baths
- Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
- Fluctuation relations and coarse-graining
- 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
- Time-Delayed Feedback control of a flashing ratchet
- Effect of time delay on feedback control of a flashing ratchet
- Harmonic Oscillator in Heat Bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark statistics
- Current fluctuations in stochastic systems with long-range memory
- An illustrative example of the relationship between dissipation and relative entropy
- Fluctuation relations for anomalous dynamics
- Delay-induced transport in a rocking ratchet under feedback control
- Information Anatomy of Stochastic Equilibria
- Fluctuation relations for driven coupled classical two-level 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
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- Uncertainty relations for time-delayed Langevin systems
- Multimode cold-damping optomechanics with delayed feedback
- Non-reciprocal hidden degrees of freedom: A unifying perspective on memory, feedback, and activity
- White-noise fluctuation theorem for Langevin dynamics
- Inference of Time-Reversal Asymmetry from Time Series in a Piezoelectric Energy Harvester
- Non-Markovian feedback control and acausality: an experimental study