Detailed fluctuation theorem bounds apparent violations of the second law

Abstract

The second law of thermodynamics is a statement about the statistics of the entropy production, $⟨\Sigma ⟩\ge 0$. For small systems, it is known that the entropy production is a random variable and negative values ($\Sigma <0$) might be observed in some experiments. This situation is sometimes called apparent violation of the second law. In this sense, how often is the second law violated? For a given average $⟨\Sigma ⟩$, we show that the strong detailed fluctuation theorem implies a lower tight bound for the apparent violations of the second law. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a bosonic mode in the weak coupling approximation, a levitated nanoparticle and a classical particle in a box.

arXiv comment5 pages, 1 figure

References in corpus (44)

• Cavity Optomechanics
• 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
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Thermodynamic uncertainty relation for biomolecular processes
• Dynamical ensembles in stationary states
• Dissipation bounds all steady-state current fluctuations
• The Nonequilibrium Thermodynamics of Small Systems
• Sub-Kelvin Parametric Feedback Cooling of a Laser-Trapped Nanoparticle
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Irreversible entropy production, from quantum to classical
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Fluctuation theorem uncertainty relation
• Thermodynamic uncertainty relations from exchange fluctuation theorems
• Fluctuation theorem for currents in open quantum systems
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Nonequilibrium fluctuations in quantum heat engines: Theory, example, and possible solid state experiments
• Generic Properties of Stochastic Entropy Production
• Unified thermodynamic uncertainty relations in linear response
• Tightening the uncertainty principle for stochastic currents
• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• The Wigner Entropy Production Rate
• Levitated Nanoparticles for Microscopic Thermodynamics - A Review
• Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
• Fluctuation Relation for Heat Engines
• Introducing one-shot work into fluctuation relations
• Optimal probabilistic work extraction beyond the free energy difference with a single-electron device
• Fluctuation theorem for the effusion of an ideal gas
• Statistical properties of entropy production derived from fluctuation theorems
• Unifying approach for fluctuation theorems from joint probability distributions
• Uncertainty relation under information measurement and feedback control
• Heat distribution of a quantum harmonic oscillator
• Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle
• Optimal processes for probabilistic work extraction beyond the second law
• Work distribution in thermal processes
• Improved bound on entropy production in a quantum annealer
• Stochastic Thermodynamics of a Particle in a Box
• Universal Property of the Housekeeping Entropy Production
• Heat distribution in open quantum systems with maximum entropy production
• Information bound for entropy production from the detailed fluctuation theorem
• Strong fluctuation theorem for nonstationary nonequilibrium systems
• Stochastic thermodynamics of nonharmonic oscillators in high vacuum

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• Finite-time bounds on the probabilistic violation of the second law of thermodynamics