Abstract
According to the second law of thermodynamics, for every transformation performed on a system which is in contact with an environment of fixed temperature, the average extracted work is bounded by the decrease of the free energy of the system. However, in a single realization of a generic process, the extracted work is subject to statistical fluctuations which may allow for probabilistic violations of the previous bound. We are interested in enhancing this effect, i.e. we look for thermodynamic processes that maximize the probability of extracting work above a given arbitrary threshold. For any process obeying the Jarzynski identity, we determine an upper bound for the work extraction probability that depends also on the minimum amount of work that we are willing to extract in case of failure, or on the average work we wish to extract from the system. Then we show that this bound can be saturated within the thermodynamic formalism of quantum discrete processes composed by sequences of unitary quenches and complete thermalizations. We explicitly determine the optimal protocol which is given by two quasi-static isothermal transformations separated by a finite unitary quench.
Highlights
In classical thermodynamics[1] the (Helmholtz) free energy of a system at thermal equilibrium is defined as F := U − TS, where U is the internal energy, T is the temperature and S is the entropy
In this paper we studied single-shot thermodynamic processes focusing on the specific task of probabilistically extracting more work than what is allowed by the second law of thermodynamics
We found that for all processes obeying the Jarzynski identity, there exists an upper bound (7) to the work extraction probability which depends on: how large is the desired violation, the minimum work that we are willing to extract in case of failure, and the free energy difference between the final and initial states
Summary
In classical thermodynamics[1] the (Helmholtz) free energy of a system at thermal equilibrium is defined as F := U − TS, where U is the internal energy, T is the temperature and S is the entropy. In our analysis we shall focus on processes obeying the Jarzynski identity[11,13,14,15] which include all those transformations where a system originally at thermal equilibrium evolves under an externally controlled, time-dependent Hamiltonian and proper concatenations of similar transformations In this context, as a first step we identify an upper bound for the probability of work extraction above the threshold Λwhich depends on the minimum amount of work Wmin that we are willing to extract in case of failure of the procedure. Explicit examples are presented in the context of discrete thermal processes[19,20] and in the context of one-molecule Szilard-like heat engines[21]
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