A unified description of two theorems in non-equilibrium statistical mechanics: The fluctuation theorem and the work relation

The fluctuation theorem (FT) and the work relation (WR) are two relations that extend our understanding of thermodynamics to non-equilibrium systems. While often treated as distinct relations, they are in fact closely related. In this letter we generalise these relations, showing that they are fundamental relations of statistical systems, and use these generalised forms to connect the FT and WR through a new set of relations, the conjugate work relations. We then take these general forms of the FT and WR, and show that they reduce to original forms under deterministic dynamics, before finally exploring their application to an experimental system.