Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form

Abstract

Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here, for the first time, we measure experimentally this function. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a two-state system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds.

arXiv comment9 pages, 3 figures, and supplemental material

References in corpus (39)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• The Physics of Maxwell's demon and information
• Dissipation: The phase-space perspective
• The Fluctuation Theorem as a Gibbs Property
• High-precision test of Landauer's principle in a feedback trap
• Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure
• Second law and Landauer principle far from equilibrium
• On the (Boltzmann) Entropy of Nonequilibrium Systems
• The physics of forgetting: Landauer's erasure principle and information theory
• Universal features in the energetics of symmetry breaking
• Refined Second Law of Thermodynamics for fast random processes
• Inconsistent thermostatistics and negative absolute temperatures
• The work value of information
• Complementarity relation for irreversible process derived from stochastic energetics
• Fluctuation Relations for Diffusion Processes
• Experimental demonstration of information to energy conversion in a quantum system at the Landauer Limit
• Thermodynamic and Logical Reversibilities Revisited
• Memory erasure in small systems
• Erasure without work in an asymmetric, double-well potential
• Axiomatic relation between thermodynamic and information-theoretic entropies
• Recovery of free energy branches in single molecule experiments
• Virtual potentials for feedback traps
• Information and thermodynamics: Experimental verification of Landauer's erasure principle
• Detailed Jarzynski Equality applied on a Logically Irreversible Procedure
• Science of Chaos or Chaos in Science?
• Time-Reversal and Entropy
• A selection of nonequilibrium issues
• Reflection positivity and phase transitions in lattice spin models
• Real-time calibration of a feedback trap
• Arbitrarily slow, non-quasistatic, isothermal transformations
• Comparison of free energy estimators and their dependence on dissipated work
• Hamiltonian derivation of a detailed fluctuation theorem
• A note on the Landauer principle in quantum statistical mechanics
• Conditional entropy and Landauer principle
• Feedback traps for virtual potentials

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• Current fluctuations and transport efficiency for general Langevin systems
• Finite-time Landauer principle
• First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Entropic bounds on currents in Langevin systems
• Optimal finite-time bit erasure under full control
• Nanoscale virtual potentials using optical tweezers
• Efficiency fluctuations and noise induced refrigerator-to-heater transition in information engines
• Thermodynamic cost and benefit of memory
• The metastable Mpemba effect corresponds to a non-monotonic temperature dependence of extractable work
• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects
• Optical tweezers as a mathematically driven spatio-temporal potential generator
• Entropy production for coarse-grained dynamics
• Extreme reductions of entropy in an electronic double dot
• Quantum Fluctuation Theorems
• Harnessing Fluctuations in Thermodynamic Computing via Time-Reversal Symmetries
• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• Cooperative quantum information erasure
• Dissipation reduction and information-to-measurement conversion in DNA pulling experiments with feedback protocols
• Optimal work extraction and mutual information in a generalized Szilárd engine
• Maximum entropy production as a necessary admissibility condition for the fluid Navier-Stokes and Euler equations
• Comparative Microscopic Study of Entropies and their Production
• Optimal Work Extraction and the Minimum Description Length Principle
• Thermodynamics of majority-logic decoding in information erasure
• Hamiltonian Memory: An Erasable Classical Bit
• Inferring entropy production from time-dependent moments
• Partially Observable Szilard Engines
• Erasing a majority-logic bit
• Nonequilibrium free energy during polymer chain growth