Laws, and symmetry

So, i bought a cup of coffee. It was hot, and quite uncomfortable on my hands. So i wonder to myself what is it about the arrangments of atoms and molecules engaging in constant motion translates to the sensation in my hands. So, look, the the cup+ coffee in my hands are an arrangement of small tiny atoms, and molecules engaged in a dance that is not at all random. If we can, each particle can be supposed to take on a trajectory, or history that is completely determined by three pieces of information. They are:

1) the dynamical Law L( Let ` s use newton ` s laws for our purpose, because it does not matter that much).
2) The initial velocity.
3)The initial position.

Where 2, and 3 are necessary because of 1.

If we can isolate the cup+coffee particles from the rest of the universes, so that no momentum is transfered between cup+ coffee, and the rest of the universe. What do i know? In theoritical physics, there is something called neother` s theorm that say that every conservational quantity corresponds to a symmetry, and vise versa. The symmetry of the cup+coffee is determined by the form of the law L that determines the precise evolution a particle in the cup+coffee. Because the form of the law L do not depend on a precise time, this is itself a symmetry. If you think about it. There is no precise reason why the form of the law L, need only 2, and 3 to determined a trajectory. In a different universe, a particle trajectory might be determined by a law that take into consideration acceration, velocity, and position. In any case, the conserved quantity due to this symmetry is energy. The uncomfortable feeling in my hands is due the energy in the form of kinetic energy of the molecules.