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This paper treats the simple example of heating a system from a given initial to a given final temperature with minimum entropy production. The allowed control for the process is the selection of  K  temperatures for intermediate heat baths. The problem is sufficiently simple to allow analytic approaches and we compare the optimal solution with the solution prescribed by equal thermodynamic distance (ETD). We find that ETD coincides with the optimum if the heat capacity is constant. For a temperaturedependent heat capacity, ETD deviates from the exact optimum. ETD however matches the optimal solution to second order in 1/ K .

A Simple Example of Control to Minimize Entropy Production