How Does the Kinetic Energy Sum Relate to Total Energy in a System of Particles?

Petar Mali
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\sum^{3N}_{i=1}\frac{p^2_i}{2m}\leq E

Why I can write this inequality? Is this E energy of system?
 
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Petar Mali said:
\sum^{3N}_{i=1}\frac{p^2_i}{2m}\leq E

Why I can write this inequality? Is this E energy of system?

For system of N identical linear harmonic oscilators of mass m, frequency \omega find phase volume, entropy and energy per particle.

H(p,x)=\sum^{N}_{i=1}\frac{p^2_i}{2m}+\frac{1}{2}\sum^{N}_{i=1}m\omega^2x^2\leq E

Why inequality? Can I get some explanation?

Thanks!
 
The second sum can't be negative.
 
I don't really know too much but...

\sum^{3N}_{i=1}\frac{p^2_i}{2m}\leq E

Looks like it's saying that the sum of the kinetic energy is less than or equal to the total energy, which makes sense to me.
 

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