Transient and asymptotic fluctuation theorems for time-inhomogenous processes

The primary subject of this dissertation are the fluctuation theorems of nonequilibrium statistical physics. These theorems, which govern the fluctuations of irreversible thermodynamic quantities such as entropy production and dissipated work, have achieved a prominent status in the field not only as the only general results to hold for systems evolving arbitrarily far from equilibrium, but because of their promise to resolve Loschmidt's paradox: that microscopically reversible dynamics can yield macroscopically irreversible phenomena. In chapter 3 we extend the asymptotic fluctuation theorem (AFT) for the first time to time-inhomogeneous continuous-time processes, considering specifically a Markov chain driven by periodic transition rates. We show that for both the time-averaged entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of its large deviation rate function generalizes to an analogous relation between the rate functions under the original process and its corresponding backward process, in which the trajectory and driving protocol have been time-reversed. This reveals that the distributions of fluctuations of thermodynamic quantities in universes where time moves forwards and backwards are interrelated. We also obtain the asymptotic time-averaged entropy production as the integral of a periodic entropy production rate. In chapter 4 we derive a measure-theoretic identity that underlies all transient fluctuation theorems (TFTs) for entropy production and dissipated work. This identity is used to deduce a tautological physical interpretation of TFTs in terms of the arrow of time, from which it follows that Loschmidt's paradox can be recast from a dynamics problem to one of the mathematical representation. We finally prove that the moment generating functions appearing in the identity fail to converge in general in a neighborhood of the origin, with the implication that thermodynamic quantities that satisfy a TFT over all timescales may fail to satisfy an AFT for any speed of the corresponding large deviation principle. In chapter 5 we consider a different topic in nonequilibrium physics - the passage times of particles in a nonconservative zero-range process to a target site. We solve for the distribution of kth passage times under both bulk and surface dynamics, using both direct probabilistic and generating function approaches.