A generalization of the martingale property of entropy production in stochastic systems

By decoupling forward and backward stochastic trajectories, we develop a family of martingales and work theorems for the same stochastic process. We achieve this by introducing an alternative work theorem derivation that uses tools from stochastic calculus instead of path integrals. Our derivation applies to both overdamped and underdamped Langevin dynamics and generalizes work theorems so that they connect new quantities in stochastic processes, potentially revealing new applications in dissipative systems.