When a Longer Path Requires Less Time—The Mpemba Pendulum

The name “Mpemba effect” was given to the finding that “the state that is initially more distant from the equilibrium state may come to the latter earlier”. It may seem that this assertion violates fundamental laws of physics and chemistry, but it has been supported by many experiments on various systems, from water to quantum dots, and discussed in many articles published in leading scientific journals. In fact, the above statement is not as paradoxical as it may seem, since it is well known that a harmonic oscillator comes to its equilibrium point in a time independent of its initial displacement. This gives us a possibility to outline the simplest equation of motion describing systems (in particular, molecular systems) capable of demonstrating the Mpemba-like effects.