Abstract
In stochastic thermodynamics work is a random variable whose average is bounded by the change in the free energy of the system. In most treatments, however, the work reservoir that absorbs this change is either tacitly assumed or modelled using unphysical systems with unbounded Hamiltonians (i.e. the ideal weight). In this work we describe the consequences of introducing the ground state of the battery and hence — of breaking its translational symmetry. The most striking consequence of this shift is the fact that the Jarzynski identity is replaced by a family of inequalities. Using these inequalities we obtain corrections to the second law of thermodynamics which vanish exponentially with the distance of the initial state of the battery to the bottom of its spectrum. Finally, we study an exemplary thermal operation which realizes the approximate Landauer erasure and demonstrate the consequences which arise when the ground state of the battery is explicitly introduced. In particular, we show that occupation of the vacuum state of any physical battery sets a lower bound on fluctuations of work, while batteries without vacuum state allow for fluctuation-free erasure.
Highlights
The second law of thermodynamics sets limits for all physical processes
While we corroborate the intuition that the battery with vacuum essentially behaves like the ideal weight in the high energy regime, we investigate quantitatively different predictions to which it leads in the low-energy regime, in particular with respect to Jarzynski equality, second law of thermodynamics and fluctuations of work
A question arises: what are the consequences of these limitations, and most importantly, what are their implications for general thermodynamic protocols? Here we provide a partial answer to this problem
Summary
The second law of thermodynamics sets limits for all physical processes. It determines which state transformations are possible, regardless of the mi-. The ideal weight model is a common way of defining work in the quantum regime which was considered for the first time in [24] and utilized to prove several fundamental results in the field of quantum thermodynamics [9, 10, 25,26,27] This additional assumption has powerful physical implications: it assures that work satisfies the second law of thermodynamics [27] and leads to the Jarzynski equality [9]. In the part of the paper we show that our model correctly reproduces the single-shot results on the work of formation originally derived using qubit as the battery system [29] This answers an open problem from the field of quantum thermodynamics by showing that the notions of singleshot and fluctuating work can be both properly defined and studied for a battery with a ground state. We finish the paper with a short summary and present several related open problems which we believe to be relevant for the field of quantum thermodynamics
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