Entropy is basically a measure of the number of avaible microstates a system can have, given a certain energy of the system. It is a measure of the uncertainty of the exact state of the system. Now, suppose we have a box with a single particle inside and with the only internal energy being the kinetic energy of the particle. What happens with the entropy as we increase the kinetic energy of the particle? If it were a molecule, an increase in energy might lead to extra degrees of freedom in form of vibrations etc. But this is not the case now. edit: Think I figured it out. Of course the "volume" in p-space of possible momenta increases, i.e, the 2-sphere has a greater area if we increase the magnitude of the momenta as a result of an increase in kinetic energy. And so the entropy must increase.