Why Are Some States More Probable in Thermal Equilibrium?

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SUMMARY

The discussion centers on the postulate of equal a priori probabilities in thermal equilibrium, specifically regarding N non-interacting simple harmonic oscillators. Participants debate the likelihood of phase space states with single particle momenta (p) near zero compared to those near maximum momentum (pmax). It is concluded that while particles near p = 0 do spend more time in that region, the overall number of available states influences the probabilities, suggesting that states minimizing total kinetic energy are indeed more probable due to statistical mechanics principles.

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bobloblaw
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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
 
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bobloblaw said:
SInce particles near p = 0 spend more time in that neighborhood.
Why?
bobloblaw said:
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.
 

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