Constant thermodynamic speed for minimizing entropy production in thermodynamic processes and simulated annealing

For an arbitrary finite-time thermodynamic or information-based process we derive a lower bound on cumulative entropy production, as well as the associated optimal operating strategy for minimizing entropy production. The optimal path corresponds to a fixed rate of entropy production in the system, provided the rate of change is calculated in terms of the natural dimensionless time scale of the system. The constant thermodynamic speed algorithm for simulated annealing is derived from first principles and shown to be the leading term in a general expansion which represents the optimal solution. The results are valid for uniform systems (no spatial gradients) in which the involved intensive thermodynamic quantities are uniquely defined. The method and conclusions are easily extended to other objective functions, such as minimal loss of availability, and to assorted thermodynamic control variables.