Microscopically Reversible Pathways with Memory

Statistical mechanics is a physics theory that deals with ensembles of microstates system compatible environmental constraints and on average define thermodynamic state. The evolution small normally subjected to changing constraints, as set by protocol, involves stochastic dependence previous events. Here, we generalize the dynamic trajectories described realization physical without dissipation include those in which history events necessary understand its future. This framework then used characterize processes experienced system, derived from ensemble averages over available pathways. We find pathways traces presence protocol entail different statistics absence prove both types are equivalent limit independent Such equivalence implies cannot evolve away equilibrium memory. These results useful interpret single-molecule experiments biophysics other fields nanoscience, well an adequate platform describe non-equilibrium processes.