Why Are Some States More Probable in Thermal Equilibrium?

[bobloblaw]

Hey guys a simple question about the postulate about equal a priori probabilites in thermal equilibrium in statistical mechanics.

I was thinking about the case of N non-interacting simple harmonic oscillators in thermal equilibrium. Shouldn't those phase space states that have single particle states with p near zero be more probable than those states with p near pmax? SInce particles near p = 0 spend more time in that neighborhood. I guess more generally wouldn't those phase states for which the total kinetic energy is minimized being more likely? I assume I'm not thinking about this properly but I can't

 

[mfb]

SInce particles near p = 0 spend more time in that neighborhood.

Why?

I guess more generally wouldn't those phase states for which the total kinetic energy is minimized being more likely?

The number of available states wins against probabilities to find some specific state - up to the average energy of the particles.