The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics

Citation

Bartolotta, Anthony Leo (2018) The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/F7VT-7X41. https://resolver.caltech.edu/CaltechTHESIS:05312018-124004005

Abstract

Quantum field theory is the language used to describe nature at its most fundamental scales; while thermodynamics is a framework to describe the collective behavior of macroscopic systems. Recent advances in non-equilibrium thermodynamics have enabled this framework to be applied to smaller systems operating out of thermal equilibrium. This thesis is concerned with both quantum field theory and non-equilibrium thermodynamics independently and with their intersection.

First, a purely phenomenological application of quantum field theory is explored in the context of the upcoming Mu2E experiment. This experiment will look for rare decays which would indicate the presence of physics beyond the Standard Model. Using the language of effective field theories, a next-to-leading order analysis of the conversion rate is performed.

The focus then shifts to an apparent paradox in the Bayesian interpretation of statistical mechanics. For a Bayesian observer making measurements of an open system, the Shannon entropy decreases, in apparent violation of the Second Law of Thermodynamics. It is shown that rather than utilizing the entropy, which can decrease under Bayesian updates, the Second Law for a Bayesian observer can be rephrased in terms of a cross-entropy which is always non-negative.

Finally, the intersection of quantum field theory and non-equilibrium thermodynamics is examined. Using quantum work fluctuation theorems, an investigation of how these frameworks can be applied to a driven quantum field theory is performed. For a time-dependent variant of λφ⁴ , analytic expressions for the work distribution functions at one-loop order are derived. These expressions are shown to satisfy the quantum Jarzynski equality and Crooks fluctuation theorem.

Thesis Files