Abstract
A system in thermal equilibrium with a bath will generally be in an athermal state, if the system-bath coupling is strong. In some cases, it will be possible to extract work from that athermal state, after disconnecting the system from the bath. We use this observation to devise a battery charging and storing unit, simply consisting of a system, acting as the battery, and a bath. The charging cycle---connect, let thermalize, disconnect, extract work---requires very little external control and the charged state of the battery, being a part of global thermal equilibrium, can be maintained indefinitely and for free. The efficiency, defined as the ratio of the extractable work stored in the battery and the total work spent on connecting and disconnecting, is always $\leq 1$, which is a manifestation of the second law of thermodynamics. Moreover, coupling, being a resource for the device, is also a source of dissipation: the entropy production per charging cycle is always significant, strongly limiting the efficiency in all coupling strength regimes. We show that our general results also hold for generic microcanonical baths. We illustrate our theory on the Caldeira-Leggett model with a harmonic oscillator (the battery) coupled to a harmonic bath, for which we derive general asymptotic formulas in both weak and ultrastrong coupling regimes, for arbitrary Ohmic spectral densities. We show that the efficiency can be increased by connecting several copies of the battery to the bath. Finally, as a side result, we derive a general formula for Gaussian ergotropy, that is, the maximal work extractable by Gaussian unitary operations from Gaussian states of multipartite continuous-variable systems.
Highlights
The second law of thermodynamics, as per the KelvinPlanck formulation [1], states that no work can be extracted in a cyclic manner from a system in thermal equilibrium
The efficiency, defined as the ratio of the extractable work stored in the battery and the total work spent on connecting and disconnecting, is always 1, which is a manifestation of the second law of thermodynamics
We investigated the arguably simplest model of charging a battery: a system in strong contact with a bath, jointly evolving towards global thermal equilibrium
Summary
The second law of thermodynamics, as per the KelvinPlanck formulation [1], states that no work can be extracted in a cyclic manner from a system in thermal equilibrium. At the beginning of the cycle, the state of the total system is not thermal—especially when the bath is not in a canonical (a.k.a., Gibbs) state, e.g., when it is in a microcanonical state—and may be active, we show for a generic thermalizing bath that, due to cyclicity, the total work one has to spend on connecting and disconnecting the system from the bath, Wc:d, is always larger than the maximal work one can extract from the system after it is detached from the bath, i.e., its ergotropy E This means that the efficiency, defined as the ratio of the energy one is able to extract and the energy one has to invest for that: η := E/Wc:d, is 1. Our device utilizes an energy storage mechanism which is not characteristic of the conventional molecular motors and force-to-force converters
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
