#### Date of Thesis

2017

#### Thesis Type

Honors Thesis

#### Degree Type

Bachelor of Science

#### Major

Physics

#### First Advisor

Benjamin P. Vollmayr-Lee

#### Keywords

non-equilibrium, field theory, work relations, chemical reactions, Jarzynski relation

#### Abstract

We develop a field theoretic description of non-equilibrium chemical work relations,generalizing the well-known Jarzynski equality using Doi-Peliti field theory. The Jarzynski equality relates the average non-equilibrium work performed on a system to the equilibrium free energy. We consider classical particles undergoing detailed balanced diffusion and chemical reactions in a local potential. The particles are coupled to a chemostat, which is a reservoir of particles, and also a thermal reservoir.Work protocols are imposed by varying the local potential, which drives the system out of equilibrium. We derive the Jarzynski relation in both the Doi representation and in the Doi-Peliti field theory. The Doi representation is a rewriting of the dynamics in terms of creation and annihilation operators, and Doi-Peliti Field theory is an extension of the Doi representation that is convenient for going to the spatial continuum limit. The Jarzynski equality is recovered in the Doi representation due to conditions set by detailed balance. Work relations, in the field theory, appear simply as a result of a gauge-like transformation combined with time reversal. We present the derivation with a one-dimensional system on a lattice and two species of particles but it can be generalized to multiple dimensions with N species of particles. We expect this formalism to be useful in describing spatial chemical reaction networks,for example, sodium-potassium pumps which are distributed along a cell membrane and consume ATP.

#### Recommended Citation

Pham, Jonathan, "A Field Theoretic Description of Non-Equilibrium Chemical Work Relations" (2017). *Honors Theses*. 401.

https://digitalcommons.bucknell.edu/honors_theses/401