Thermodynamic entropic uncertainty relation

Abstract

Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory, Shannon entropy is a common measure of uncertainty. However, a clear quantitative relationship between the Shannon entropy of an observable and the entropy production in stochastic thermodynamics remains to be established. In this Letter, we show that an uncertainty relation can be formulated in terms of the Shannon entropy of an observable and the entropy production. We introduce symmetry entropy, an entropy measure that quantifies the symmetry of the observable distribution, and demonstrate that a greater asymmetry in the observable distribution requires higher entropy production. Specifically, we establish that the sum of the entropy production and the symmetry entropy cannot be less than $\ln 2$. As a corollary, we also prove that the sum of the entropy production and the Shannon entropy of the observable is no less than $\ln 2$. As an application, we demonstrate our relation in the diffusion decision model, revealing a fundamental trade-off between decision accuracy and entropy production in stochastic decision-making processes.

10 pages, 5 figures; 3 pages of supplementary material

References in corpus (31)

• 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
• Thermodynamic uncertainty relation for biomolecular processes
• The Uncertainty Principle in the Presence of Quantum Memory
• Dissipation bounds all steady-state current fluctuations
• Entropic Uncertainty Relations and their Applications
• An improved Landauer Principle with finite-size corrections
• Speed Limit for Classical Stochastic Processes
• Fluctuation theorem uncertainty relation
• Current fluctuations and transport efficiency for general Langevin systems
• Thermodynamics of precision in quantum non equilibrium steady states
• Unravelling the large deviation statistics of Markovian open quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Thermodynamic uncertainty relation for time-dependent driving
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
• Quantum thermodynamic uncertainty relation for continuous measurement
• Uncertainty relations in stochastic processes: An information inequality approach
• Kinetic uncertainty relation
• Stochastic thermodynamic interpretation of information geometry
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Thermodynamic uncertainty relation for general open quantum systems
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Thermodynamic uncertainty relation in thermal transport
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Role of Quantum Coherence in Kinetic Uncertainty Relations
• Thermodynamic concentration inequalities and tradeoff relations
• Tradeoff relations in open quantum dynamics via Robertson, Maccone-Pati, and Robertson-Schrödinger uncertainty relations