On the form of prior for constrained thermodynamic processes with uncertainty

Abstract: We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely values of the uncertain parameters.The priors are derived explicitly for both the entropy conserving and the energy conserving processes. The proposed form is useful when the constraint equation cannot be treated analytically. The inference is performed using spin-1/2 systems as models for heat reservoirs. Analytical results are derived in the high temperatures limit. Comparisons are found between the estimates of thermal quantities and the optimal values described by extremum principles. We also seek a intuitive interpretation of the prior and show that it becomes uniform over the quantity which is conserved in the process. We find further points of correspondence between the inference based approach and the thermodynamic framework.