Work fluctuations due to partial thermalizations in two-level systems

Abstract

We study work extraction processes mediated by finite-time interactions with an ambient bath -- \emph{partial thermalizations} -- as continuous time Markov processes for two-level systems. Such a stochastic process results in fluctuations in the amount of work that can be extracted and is characterized by the rate at which the system parameters are driven in addition to the rate of thermalization with the bath. We analyze the distribution of work for the case where the energy gap of a two-level system is driven at a constant rate. We derive analytic expressions for average work and lower bound for the variance of work showing that such processes cannot be fluctuation-free in general. We also observe that an upper bound for the Monte Carlo estimate of the variance of work can be obtained using Jarzynski's fluctuation-dissipation relation for systems initially in equilibrium. Finally, we analyse work extraction cycles by modifying the Carnot cycle, incorporating processes involving partial thermalizations and obtain efficiency at maximum power for such finite-time work extraction cycles under different sets of constraints.

arXiv comment16 pages, 12 figures, 4 appendices

References in corpus (24)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Quantum Thermodynamic Cycles and quantum heat engines
• The Nonequilibrium Thermodynamics of Small Systems
• Efficiency at maximum power of low dissipation Carnot engines
• The thermodynamic meaning of negative entropy
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Thermalizing Quantum Machines: Dissipation and Entanglement
• A simple model of quantum trajectories
• Truly work-like work extraction
• The work value of information
• The Minimal Work Cost of Information Processing
• Work fluctuations in slow processes: quantum signatures and optimal control
• Collision models in quantum optics
• Quantum work statistics close to equilibrium
• Universal constraint for efficiency and power of a low-dissipation heat engine
• Maximum Efficiency of Low-Dissipation Heat Engines at Arbitrary Power
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Optimal operating protocol to achieve efficiency at maximum power of heat engines
• Avoiding irreversibility: engineering resonant conversions of quantum resources
• Imperfect Thermalizations Allow for Optimal Thermodynamic Processes
• Work distribution functions for hysteresis loops in a single-spin system
• One-shot information-theoretical approaches to fluctuation theorems

Cited by in corpus (2)

• Quantum collision models: open system dynamics from repeated interactions
• Cyclic quantum engines enhanced by strong bath coupling