Extraction of ergotropy: free energy bound and application to open cycle engines

Abstract

The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by microscopic machines. We provide the fundamental bound on the amount of ergotropy which can be extracted from environment in this way. The bound is expressed in terms of the non-equilibrium free energy difference and can be saturated in the limit of infinite dimension of the system's Hamiltonian. The ergotropy extraction process leading to this saturation is numerically analyzed for finite dimensional systems. Furthermore, we apply the idea of extraction of ergotropy from environment in a design of a new class of stroke heat engines, which we label open-cycle engines. Efficiency and work production of these machines can be completely optimized for systems of dimensions 2 and 3, and numerical analysis is provided for higher dimensions.

31 pages, 6 figures. Comments welcome

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• The thermodynamic meaning of negative entropy
• Dissipative charging of a quantum battery
• Bound on Ergotropic Gap for Bipartite Separable States
• Thermodynamic Signatures of Genuinely Multipartite Entanglement
• Quantum and classical ergotropy from relative entropies
• The tight Second Law inequality for coherent quantum systems and finite-size heat baths
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• Catalytic advantage in Otto-like two-stroke quantum engines
• Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
• Catalytic enhancement in the performance of the microscopic two-stroke heat engine
• Quantum thermodynamic advantage in work extraction from steerable quantum correlations
• Spectral Bounds on Entropy and Ergotropy via Statistical Effective Temperature in Classical Polarization and Quantum Thermal States
• Optimal performance of a three stroke heat engine in the microscopic regime
• Work Fluctuations in Ergotropic Heat Engines
• Measuring work in quantum many-body systems using a dynamical "work agent"
• Ergotropic advantage in a measurement-fueled quantum heat engine
• Charge-Preserving Operations in Quantum Batteries
• Photonic Energy-Coherence Theorem and Experimental Validations