Hurst-Kolmogorov dynamics as a result of extremal entropy production

► Extremization of entropy production is useful in stochastic representations of natural systems.► The entropy production could be more effectively defined in logarithmic time. ► Extremization of entropy production results in Hurst-Kolmogorov dynamics. ► Real world data illustrate the plausibility of this finding. ► The results are useful in estimating future uncertainty and in planning and design.