  We quantify the prior information to infer the optimal characteristics for a
constrained thermodynamic process of maximum work extraction for a pair of
non-identical finite systems. The total entropy of the whole system remains
conserved. The ignorance is assumed about the final temperature of the finite
systems and then a prior distribution is assigned to the unknown temperatures.
We derive the estimates of efficiency for this reversible model of heat engine
with incomplete information. The estimates show good agreement with efficiency
at optimal work for arbitrary sizes of systems, however the estimates become
exact when one of the reservoir becomes very large in comparison to the other.

Statistical Mechanics