  In addition to the Riemannian metricization of the thermodynamic state space,
local relaxation times offer a natural time scale, too. Generalizing existing
proposals, we relate {\it thermodynamic} time scale to the standard kinetic
coefficients of irreversible thermodynamics. Criteria for minimum entropy
production in slow, slightly irreversible processes are discussed.
Euler-Lagrange equations are derived for optimum thermodynamic control for
fixed clock-time period as well as for fixed {\it thermodynamic} time period.
Only this latter requires constant thermodynamic speed as the optimum control
proposed earlier. An easy-to-implement stepwise algorithm is constructed to
realize control at constant thermodynamic speed. Since thermodynamic time is
shown to correspond to the number of steps, thus the sophisticated task of
determining thermodynamic time in real control problems can be substituted by
measuring ordinary intensive variables. Most remarkably, optimum paths are
Riemannian geodesics which would not be the case had we used ordinary time.
