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I am new to Statistical Mechanics, and have just started reading from this book Tony Genault Statistical Physics where he writes the following (paraphrased for convenience)-

Consider a system of $N$ weakly interacting particles. If the energy of one particle is $\epsilon$, the total energy of the system is- $$U=\sum_{l=1}^{N} \epsilon(l)$$ Any such expression implies that the interaction energies between particles are much smaller than these (self) energies ε. Actually any thermodynamic system must have some interaction between its particles, otherwise it would never reach equilibrium. The requirement rather is for the interaction to be small enough for the above equation to be valid, hence ‘weakly interacting’ rather than ‘non-interacting’ particles.

And hence my question- Why does non interacting not work?

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  • $\begingroup$ Ask yourself what would equilibrium (or non-equilibrium) mean between two systems if they do not interact? Can it be any meaning to that question? $\endgroup$ – hyportnex Mar 15 at 15:59
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Non-interacting in this context means the particles cannot collide and exchange kinetic energy. Without the ability to share energy during collisions, the system of particles has no opportunity to distribute the individual energies of the particles between all those particles and hence cannot eventually achieve a maxwell-boltzmann energy distribution, the peak value of which defines the temperature of the ensemble.

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  • $\begingroup$ Right, the initial distribution of energies stays intact if no interaction happens. $\endgroup$ – Vladimir Kalitvianski Mar 15 at 5:57
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    $\begingroup$ @VladimirKalitvianski yes yes, and this is probably why dark matter halos do not fall into the centers of galaxies even after billions of years. no dissipation = no gravitational collapse $\endgroup$ – niels nielsen Mar 15 at 6:04

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