[scottmsul]

Everyone here seems totally lost on the physics connection. Suppose you have a box of atoms, each atom can be in one of two states, a low energy E1 and a high energy E2. If the box has a temperature T, then the probability that any atom is in state E1 is e^(-E1/kT) / [ e^(-E1/kT) + e^(-E2/kT) ], and similar for E2. As you lower the temperature most of the atoms gravitate towards the lower energy state E1, and as you raise the temperature they gravitate towards a 50/50 mix of E1 and E2.

[amluto]

Since you bring up physics, this has a name: the Maxwell-Boltzmann distribution. You might have trouble getting physicists to describe particles as “gravitating” to it, though — the particles are doing their own thing, and this is the resulting probability distribution.

But this is only for distinguishable particles. If you have a bunch of indistinguishable particles, you get the Fermi-Dirac distribution or the Bose-Einstein distribution, depending on whether they are fermions or bosons.

You can find all of these distributions on Wikipedia.

[kgwgk]

Fun fact: not only you get closer to a 50/50 mix of E1 and E2 (increasing temperature) but if you continue to add energy to the box you will find yourself with more atoms in the E2 state than in the E1 state.

The temperature will go from infinity to -infinity and as you keep adding energy you will approach zero temperature from the left (increasing temperature). The zero value is reached when the energy of the system can no longer be increased and all the atoms are in the E2 state.

[bobbylarrybobby]

How are you defining temperature? I assume it's not average kinetic energy of the particles. Is it that definition I learned once upon a time where T = d entropy /d energy? Is this a useful definition of temperature if it leads to this scenario?

[jbay808]

The most fun part of learning statistical mechanics was un-learning everything I had learned about temperature in high school!

[tpoacher]

Just because there is a physics connection doesnt make this a good name for the parameter.

I do understand the benefit of not having 10 different names for the same concept under different scenarios, however. Even if that name isnt the best.

But note that, even in the physics scenario, temperature isnt really the name providing the most intuition either. You need to be aware of the connection between higher temperature -> higher excitability/mobility to begin with, for it to make sense; and temperature isnt the only way to modify this underlying excitability in the first place.