Trajectory Class Fluctuation Theorem

TL;DR

The Trajectory Class Fluctuation Theorem (TCFT) enhances the Second Law of Thermodynamics by providing stronger bounds, improving free energy estimates, and diagnosing information processing in thermodynamic systems through a unified framework.

Contribution

The paper introduces the TCFT, a new theorem that unifies and extends existing fluctuation theorems to better analyze thermodynamics of system trajectories.

Findings

Strengthens the Second Law bounds on resource fluxes.

Improves empirical free energy estimation methods.

Diagnoses successful and failed information processing in experiments.

Abstract

The Trajectory Class Fluctuation Theorem (TCFT) substantially strengthens the Second Law of Thermodynamics -- that, in point of fact, can be a rather weak bound on resource fluxes. Practically, it improves empirical estimates of free energies, a task known to be statistically challenging, and has diagnosed successful and failed information processing in experimentally-implemented Josephson-junction information engines. The development here justifies that empirical analysis, explicating its mathematical foundations. The TCFT reveals the thermodynamics induced by macroscopic system transformations for each measurable subset of system trajectories. In this, it directly combats the statistical challenge of extremely rare events that dominate thermodynamic calculations. And, it reveals new forms of free energy -- forms that can be solved for analytically and practically estimated. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks' Detailed Fluctuation Theorem (single trajectories) to Jarzynski's Equality (trajectory ensembles).