Abstract
The fluctuation theorems, and in particular, the Jarzynski equality, are the most important pillars of modern non-equilibrium statistical mechanics. We extend the quantum Jarzynski equality together with the Two-Time Measurement Formalism to their ultimate range of validity -- to quantum field theories. To this end, we focus on a time-dependent version of scalar phi-four. We find closed form expressions for the resulting work distribution function, and we find that they are proper physical observables of the quantum field theory. Also, we show explicitly that the Jarzynski equality and Crooks fluctuation theorems hold at one-loop order independent of the renormalization scale. As a numerical case study, we compute the work distributions for an infinitely smooth protocol in the ultra-relativistic regime. In this case, it is found that work done through processes with pair creation is the dominant contribution.
Highlights
In physics there are two kinds of theories to describe motion: microscopic theories whose range of validity is determined by a length scale and the amount of kinetic energy, such as classical mechanics or quantum mechanics; and phenomenological theories, such as thermodynamics, which are valid as long as external observables remain close to some equilibrium value
While quantum field theories were originally developed for particle physics and cosmology, this approach has been shown to be powerful in the description of condensed matter systems
Because of the form of the work distributions, it is straightforward to show that the fluctuation theorems hold if one removes the loop corrections and in the nonrelativistic limit. These results demonstrate that quantum fluctuation theorems and stochastic thermodynamics can be extended to include quantum field theories, our most fundamental theory of nature
Summary
In physics there are two kinds of theories to describe motion: microscopic theories whose range of validity is determined by a length scale and the amount of kinetic energy, such as classical mechanics or quantum mechanics; and phenomenological theories, such as thermodynamics, which are valid as long as external observables remain close to some equilibrium value. It is important to remark that in complete analogy to how classical mechanics is contained in quantum mechanics (in the appropriate limits), the twotime measurement formalism produces work distribution functions which correspond to those of classical systems in semiclassical approximations [41,42,43,44,45] To date another decade has gone by, yet quantum stochastic thermodynamics is still rather incomplete. We discuss the analytic properties of the work distribution function in Sec. VII and analytically verify both the Crooks fluctuation theorem and quantum Jarzynski equality at leading order for time-dependent λφ.
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