Fluctuations of dynamic systems

Abstract

The fluctuation theorem quantifies the distribution of reversible and irreversible system trajectories, while the work relation connects a weighted average of the work with the free energy change for a system. Both are unusual in that they apply exactly to non-equilibrium thermodynamic systems. The aim of this work is to study the connection between these two theorems, both in theory and application. First, a general derivation of the fluctuation theorem and work relation is developed and a mathematical connection is made between their arguments, dissipation and work. We then use this approach to apply these relations to a system based on optical tweezers trapping a colloid in solution. This system is well described using both deterministic and stochastic dynamics, and enables us to undertake a number of different experiments that explore the relationship between these two theorems. These experiments verify the fluctuation theorem and work relation, but also show how the details of the experiment and the dynamics used to analyse it affect the application of these theorems and the information they provide.