Second law of thermodynamics for batteries with vacuum state

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.

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

“…In this presentation, all qubit erasure processes take place in the computational registers. It is possible to outsource this thermodynamic task to an external battery register [6,[25][26][27]. The battery consists of fueled qubits in state |0 and depleted qubits in the fully mixed state 1/2; the erasure of depleted qubits takes place there at temperature T , with an average work cost of k B T ln 2 per qubit.…”

Work and Fluctuations: Coherent vs. Incoherent Ergotropy Extraction

“…In general, for the coherent work operator (i.e., with the non-vanishing commutator (24)), the expansion of the operator MS (t) is equal to:…”

“…Consequently, we possess a framework with an explicit work reservoir that recreates all of the fluctuation theorems just by this symmetry (cf. [24] where are discussed corrections if translational invariance is violated). Moreover, it has also been shown that the optimal work extracted by the quantum weight is limited by the ergotropy [19,25], which, with the notion of passivity, is another building block of quantum thermodynamics (see, e.g., [26,27]).…”

Channels, measurements and post-selection in quantum thermodynamics

“…Other works have introduced different models of batteries, including a two-level wit [8], a weight with discrete spacing [22] or energies bounded from below [45], which lead to additional constraints on the initial state or different results in terms of work extraction. Our motivation for considering the model above is it leads to a simple model, with the closest parallels to classical thermodynamics.…”