Trajectory Class Fluctuation Theorem

Abstract

The Trajectory Class Fluctuation Theorem (TCFT) presents equalities between thermodynamic quantities, such as work costs and free energy changes, and the probabilities of classes of system-state trajectories in equilibrium-steady-state nonequilibrium processes. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks’ Detailed Fluctuation Theorem (single trajectories) to Jarzynski’s Equality (full trajectory ensembles). Leveraging coarse-grained information about how systems evolve, the TCFT provides a substantial strengthening of the Second Law of Thermodynamics—that, in point of fact, can be a rather weak bound between requisite work and free energy change. It also can be used to improve empirical estimates of free energies, a task known to be statistically challenging, by diverting attention from rare, work-dominant trajectories in convenient but highly nonequilibrium processes. The TCFT also reveals new forms of free energy useful for bounding work costs when computing with systems whose microscopic details are difficult to ascertain—forms that can be solved analytically and practically estimated. For engineered systems more generally, it connects the role of system state trajectories in system functionality to the particular work costs required to evolve those trajectories. Previously, the TCFT was used to connect the microscopic dynamics of experimentally-implemented Josephson-junction information engines with the mesoscopic descriptions of how information was processed. The development here justifies that empirical analysis, explicating its mathematical foundations.