Date of Thesis
Bachelor of Science
Benjamin P. Vollmayr-Lee
Recently, a number of strict equalities have been developed for far from equilibrium statistical mechanical systems that relate work done on a system and its change in free energy. We develop a field-theoretic description of non-equilibrium work relations using Doi-Peliti field theory. Specifically, we create the Doi-Peliti field theory for thermal systems and use it to derive the well-known Jarzynski equality. Our resulting framework can be extended to other non-equilibrium relations. We consider classical particles on a lattice that experience pair-wise interactions and a local potential. These particles hop with rates determined by coupling to a thermal bath. Work protocols are imposed by varying the local potential, which drives the system out of equilibrium. In this framework, work relations appear simply as the result of a gauge-like transformation combined with a time-reversal. We present the derivation with a one-dimensional system on a lattice and conclude with the generalization to multiple dimensions and the continuum limit.
Baish, Andrew James, "Deriving the Jarzynski Relation from Doi-Peliti Field Theory" (2015). Honors Theses. 315.