Nonequilibrium thermodynamics of uncertain stochastic processes

In real-world stochastic thermodynamics, we never have infinitely > precise knowledge of the temperatures / chemical potentials of the reservoirs, the energy spectrum, the control protocol, maybe even the number of reservoirs, etc. We investigate how such uncertainty about the precise experimental apparatus modifies the laws of stochastic thermodynamics. We first consider the case where you sample a given distribution over apparatus' once and then sample the distribution over trajectories conditioned on that apparatus an infinite number of times. This uncovers both commonalities and differences between the stochastic thermodynamics of systems with an uncertain apparatus and standard (full certainty) stochastic thermodynamics. We next consider the case where we sample an apparatus once and then generate a sequence of multiple random trajectories where we are able to modify some aspects of the apparatus from one trajectory to the next, based on information concerning the apparatus provided by the earlier trajectories. This opens a very rich set of issues concerning the thermodynamic value of information about an apparatus, extending previous work in the literature on the thermodynamic value of information about the state of the system.