Inverse thermodynamic uncertainty relation and entropy production
arXiv:2503.14204 · doi:10.1103/mf9f-nf7g
Abstract
Nonequilibrium current fluctuations represent one of the central topics in nonequilibrium physics. The thermodynamic uncertainty relation (TUR) is widely acclaimed for rigorously establishing a lower bound on current fluctuations, expressed in terms of the entropy production rate and the average current. In this study, we focus on an upper bound for the fluctuations, referred to as the inverse thermodynamic uncertainty relation (iTUR). We derive a universal iTUR expression in terms of the entropy production rate for continuous-variable systems governed by overdamped Langevin equations, as well as for discrete-variable systems described by Markov jump processes. The iTUR establishes a no-go theorem prohibiting perpetual superdiffusion in systems with a finite entropy production rate and a finite spectral gap. The divergence of the variance of any current becomes possible only when the spectral gap of the symmetrized time-evolution operator closes or the entropy production rate diverges. As a relevant experimental scenario, we apply the iTUR to the phenomenon of giant diffusion, emphasizing the pivotal roles of the spectral gap and entropy production.
References in corpus (46)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Thermodynamic uncertainty relation for biomolecular processes
- Dissipation bounds all steady-state current fluctuations
- Stochastic thermodynamics: Principles and perspectives
- Universal trade-off between power, efficiency, and constancy in steady-state heat engines
- Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
- Universal bounds on current fluctuations
- Finite-time generalization of the thermodynamic uncertainty relation
- Quantifying dissipation using fluctuating currents
- Current fluctuations and transport efficiency for general Langevin systems
- Discrete-time thermodynamic uncertainty relation
- Universal bound on the efficiency of molecular motors
- Thermodynamic uncertainty relation for time-dependent driving
- Inferring entropy production from short experiments
- Inferring dissipation from current fluctuations
- Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
- Unified thermodynamic uncertainty relations in linear response
- On the validity of the thermodynamic uncertainty relation in quantum systems
- Multidimensional thermodynamic uncertainty relations
- Quantum thermodynamic uncertainty relation for continuous measurement
- Inferring broken detailed balance in the absence of observable currents
- Estimating entropy production by machine learning of short-time fluctuating currents
- Tightening the uncertainty principle for stochastic currents
- Giant Colloidal Diffusivity on Corrugated Optical Vortices
- Thermodynamic uncertainty relation in slowly driven quantum heat engines
- Thermodynamic Uncertainty Relation for Arbitrary Initial States
- Thermodynamic uncertainty relations including measurement and feedback
- Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
- Thermodynamic uncertainty relation in thermal transport
- Thermodynamics of Precision in Markovian Open Quantum Dynamics
- A generalization of the thermodynamic uncertainty relation to periodically driven systems
- Unified thermodynamic-kinetic uncertainty relation
- Effect of a magnetic field on the thermodynamic uncertainty relation
- Classical pendulum clocks break the thermodynamic uncertainty relation
- Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
- Thermodynamic uncertainty relations for coherently driven open quantum systems
- Kinetic uncertainty relation on first passage time for accumulated current
- Symmetrized Liouvillian Gap in Markovian Open Quantum Systems
- A unifying picture of generalized thermodynamic uncertainty relations
- Uncertainty relations and fluctuation theorems for Bayes nets
- Fundamental bounds on precision and response for quantum trajectory observables
- Exact results for the finite time thermodynamic uncertainty relation
- Enhanced diffusion of molecular motors in the presence of adenosine triphosphate and external force
- Nonequilibrium thermodynamics of DNA nanopore unzipping
- Temperature anomalies of oscillating diffusion in ac-driven periodic systems
- Thermodynamic uncertainty relations in a linear system