I quote the coming lines from Igneous & Metamorphic Petrology by Myron G. Best (2003):
One statement of the second law of thermodynamics is that spontaneous natural processes tend to even out the concentration of some form of energy, smoothing the energy gradient. A hot lava flow extruded from a lofty volcano cools to atmospheric T as it descends down slope, thereby reducing differences in thermal and gravitational potential energy between initial and final states in accordance with the second law.
Eventually, billions of years from now, all of the thermal energy in the Earth will be consumed in tectonism, volcanism, and other processes and dispersed into outer space. No mountains or volcanoes will be erected and erosion in the solar powered hydrologic system will wear everything down to some common level (assuming the Sun does not run out of nuclear energy!).
Without differences in the concentration of thermal and gravitational potential energy no geologic work can be accomplished and the planet will be geologically dead! The measure of the uniformity in concentration of energy in a system is called the entropy, S. The more uniform the concentration of some form of energy, the greater the entropy. The geologically dead planet will have maximal entropy.
Is the last statement is right?... because it seems that dead planet will have the minimal entropy not the maximum, if we consider that entropy is the measure of disorder? just like ice vs water vs vapor.. ice will eventually have the minimal entropy as temperature decreases (thermal stability increases).