Abstract
Thermodynamic uncertainty relations quantifying a trade-off between current fluctuation and entropy production have been found in various stochastic systems. Herein, we study the thermodynamic uncertainty relations for Langevin systems driven by an external control protocol. Using information-theoretic techniques, we derive the uncertainty relations for arbitrary observables satisfying a scaling condition in both overdamped and underdamped regimes. We prove that the observable fluctuation is constrained by both entropy production and a kinetic term. The derived bounds are applicable to both current and noncurrent observables, and hold for arbitrary time-dependent protocols, thus, providing a wide range of applicability. We illustrate our universal bounds with the help of three systems: a dragged Brownian particle, a Brownian gyrator, and a stochastic underdamped heat engine.
Highlights
Stochastic thermodynamics [1,2,3] provides a rigorous framework for investigating the physical properties of small systems
Unlike in most previous studies, where the system is assumed to be in a stationary or in a transient regime, here, the system starts from an arbitrary distribution at time t = 0 and is subsequently driven by an external control protocol λ up to time t = τ
The results demonstrate that the fluctuations of observables are constrained by entropy production and by a kinetic term
Summary
Stochastic thermodynamics [1,2,3] provides a rigorous framework for investigating the physical properties of small systems. It is known that thermodynamic costs place fundamental limits on the performance of real-world systems, ranging from living organisms to artificial devices. Investigating such trade-off relations provides insights into the optimal design principles for such systems. Powerful inequalities known as thermodynamic uncertainty relations (TURs) have been discovered for nonequilibrium systems [4,5]. They assert a trade-off between the current fluctuation and dissipation quantified via entropy production, i.e., a high precision of currents is unattainable without increasing the associated entropy production. TURs imposed the following bound in steady-state systems, φ2 σ φ (1)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
