Now entropy is defined such as to increase whenever a natural process takes place. It stays constant if a system is in equilibrium and it decreases for the hypothetic process that goes the wrong way round. One billiard ball coming from the left hits eight balls coming from the right. In the final state the eight balls are at rest while the ball that came from the left is reflected back at high speed. One cannot tell.
Mechanical processes are at constant entropy.
So for the mentioned block that accelerates spontaneously while cooling down, entropy would decrease. The second law of thermodynamics prohibits that. Overall entropy cannot decrease. This can happen only locally if, and only if, entropy is increased somewhere else by at least, and generally more than, the same amount. Thus entropy is a quantity that reflects our empirical knowlegde about the direction of natural processes.