Microscopic Work Distribution of Small System in Quantum Isothermal Process

Abstract

For a two-level quantum mechanical system, we derive microscopically the exact expression for the fluctuation of microscopic work in a multi-step non-equilibrium process, and we rigorously prove that in an isothermal process, the fluctuation is vanishingly small, and the most probabilistic work just equals to the difference of the free energy. Our study demonstrates that the convergence of the microscopic work in the isothermal process is due to the nature of isothermal process rather than usual thermodynamic limit condition. Our investigation justifies the validity of "minimum work principle" formulation of the second law even for a small system far from thermodynamic limit.

LAUR 08-2152, 5 pages, 2 figures

References in corpus (12)

• A nonequilibrium equality for free energy differences
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Quantum Thermodynamic Cycles and quantum heat engines
• The Nonequilibrium Thermodynamics of Small Systems
• Dissipation: The phase-space perspective
• Quantum Heat Engine With Multi-Level Quantum Systems
• Fluctuation and dissipation of work in a Joule experiment
• Minimal work principle: proof and counterexamples
• On the work distribution for the adiabatic compression of a dilute classical gas
• Decoherence and Thermalization
• Resonance Theory of Decoherence and Thermalization
• Minimal Work Principle and its Limits for Classical Systems

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• Implications of Coupling in Quantum Thermodynamic Machines
• Simulating finite-time quantum isothermal processes with generic superconducting quantum circuit
• Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• The EPR Paradox Implies A Minimum Achievable Temperature
• Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold