Work Distributions on Quantum Fields

Abstract

We study the work cost of processes in quantum fields without the need of projective measurements, which are always ill-defined in quantum field theory. Inspired by interferometry schemes, we propose a work distribution that generalizes the two-point measurement scheme employed in quantum thermodynamics to the case of quantum fields and avoids the use of projective measurements. The distribution is calculated for local unitary processes performed on KMS (thermal) states of scalar fields. Crooks theorem and the Jarzynski equality are shown to be satisfied for a family of spatio-temporally localized unitaries, and some features of the resulting distributions are studied as functions of temperature and the degree of localization of the unitary operation. We show how the work fluctuations become much larger than the average as the process becomes more localized in both time and space.Introduction.-At microscopic scales average quantities no longer characterize completely the state of a system or the features of a thermodynamic process. There, stochastic or quantum fluctuations become relevant, being of the same order of magnitude as the expectation values [1][2][3]. It is therefore important to develop tools that allow us to study the properties of these fluctuations to fully understand thermodynamics at the small scales.One of the best studied quantities in this context is work of out-of-equilibrium processes, and its associated fluctuations. The notion of work is an empirical cornerstone of macroscopic equilibrium thermodynamics. However, work in microscopic quantum scenarios is a notoriously subtle concept (e.g., it cannot be associated to an observable [4]), and although there is no single definition of work distributions and work fluctuations in quantum theory, several possibilities have been proposed (see e.g., [5]). Perhaps the most established notion of work fluctuations is that defined through the Two-Point Measurement (TPM) scheme [6,7], where the work distribution of a process is obtained by performing two projective measurements of the system's energy, at the beginning and at the end of the process. The TPM formalism defines a work distribution with a number of desirable properties: it is linear on the input states, it agrees with the unambiguous classical definition for states diagonal in the energy eigenbasis, and it yields a number of fluctuation theorems in different contexts [1,7,8].An important caveat of this definition is that it cannot be straightforwardly generalized to processes involving quantum fields: projective measurements in quantum field theory (QFT) are incompatible with its relativistic nature. They cannot be localized [9], they can introduce ill-defined operations due to UV divergences and, among other serious problems, they enable superluminal signaling even in the most innocent scenarios [10]. For these reasons, it has been strongly argued that projective measurements should be banished from the formalism of any relativistic field theory [10][11][12]. However, quantum fields are cert...

Strong coupling from non-equilibrium Monte Carlo simulations

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