Question: It is very common to have uncorrelated velocities in chaotic dynamical systems. Yet, we should be wary in equating the two quite different meanings of chaos.

Instead of matching dynamical chaos to molecular chaos, it seems much easier to work the other way as the former case does not have a universal definition. Hence, if within some chaotic Hamiltonian system the velocities are uncorrelated, can we say this is molecular chaos? In other words, does molecular chaos exist when particles shrink to an infinitesimal point?

edit: The final question is obviously absurd since molecular chaos concerns uncorrelated velocities occurring as the result of *collisions* of particles. The point is that particles of finite size are not necessary to define a velocity, so does that mean the molecular chaos 'definition' can be refined further.

Answer: 
Photons (obviously) travel at the speed of light in vacuum. Any other particle with zero rest mass (such as the hypothetical [graviton](https://en.wikipedia.org/wiki/Graviton), if it exists) would also travel at the speed of light. Nothing with non-zero rest mass can travel at the speed of light in vacuum. However, particles can travel at or faster than the *local* speed of light in media such as water - see [this Wikipedia article](https://en.wikipedia.org/wiki/Cherenkov_radiation).
Nothing with rest mass can attain the speed that light travels at in vacuum.