Nonequilibrium uncertainty principle from information geometry

Abstract

With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we define is an upper bound for the entropy production and flow rates, but it does not necessarily correlate with the shortest distance to equilibrium. For a model one-bit memory device, we find that expediting the erasure protocol increases the maximum dissipated heat and geometric uncertainty. A driven version of Onsager's three-state model shows that a set of dissipative, high-uncertainty initial conditions, some of which are near equilibrium, scar the state space.

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Cited by in corpus (24)

• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Time-information uncertainty relations in thermodynamics
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Unifying Quantum and Classical Speed Limits on Observables
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Geometric distinguishability measures limit quantum channel estimation and discrimination
• Bounding generalized relative entropies: Nonasymptotic quantum speed limits
• Optimising the relaxation route with optimal control
• Information geometry approach to quantum stochastic thermodynamics
• Thermal brachistochrone for harmonically confined Brownian particles
• Speed limits of the trace distance for open quantum system
• Entropic dynamics on Gibbs statistical manifolds
• Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions
• Universal dynamic scaling in chemical reactions at and away from equilibrium
• Maximum speed of dissipation
• Information geometry of transitions between quantum nonequilibrium steady states
• Stochastic thermodynamics of Fisher information
• Contact geometry and quantum thermodynamics of nanoscale steady states
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Thermodynamic interpretation to Stochastic Fisher Information and Single-Trajectory Speed Limits
• Classical Geometric Fluctuation Relations
• Work, entropy production, and thermodynamics of information under protocol constraints
• Relations between entropy rate, entropy production and information geometry in linear stochastic systems
• Quantifying Irreversibility via Bayesian Subjectivity for Classical & Quantum Linear Maps