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Ah, but who says that negative absolute temperatures exist at all? This is not without its controversies. There's a nature paper here which challenges the very existence of negative absolute temperatures, arguing that negative temperatures come about due to a poor method of defining the entropy, which in turn is used to calculate the temperature. Other ...

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The above is the Boltzmann equation for annihilation/collisions in an expanding universe. Short answer The superscript in this case stands for equilibrium number density, as you pointed out. This means the $n_i^{(0)}$ stands for particle species $i$ number density in number density equilibrium, meaning equilibrium in which each particle species $i$ is ...

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The Question is basically "how Quickly"? It's definetly not "instantly", and there is some delay, which causes movement inside the fluid and it must take some time before viscous forces kills these movements. And as they are, by nature exponential, means the lower the velocity, the smaller the losses and thus the time can be considerably different according ...

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There are indeed internal states, but I believe that this does not affect the thermal equilibrium condition. Consider a particle with energy $E=p^2/(2m)+\epsilon_\alpha$, where $\alpha$ labels inernal states, such as the vibrational and rotational levels of an atom. The distribution function is $f_\alpha(p)$, and the phase space measure in the collision ...

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a) You're correct. Since the two carriages AND the spring can only move in one dimention, the system has only one degree of freedom. But wait. They are not moving in a plane! (that is a two domentional space), but in a straight LINE (that has only one dimention). *I know, this is only semantics. b) When you are told that the spring is based on a linear ...

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He talks about imaginary situation when **there is a point in space with stable equilibrium*. As Feynman says, it requires $E=0$ at some point $(P_0)$ and all $E$ vectors looking inwards (like local minima) around that point. Then let's use Gauss's law: compute flux. It will definitely be not zero, which means that such point does not exist. What is ...

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