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I've done my statistical mechanics course, but still. Whenever I see the temperature, a question pops up in my head! So I'm curious to see if someone can help me with this obsession!

Temperature is defined as

T = (dS/dE)^-1

S: amount of accessible microstates

E: energy

1) temperature is defined at equilibrium. this should mean approximately constant energy. yet this definition implies a variation of energy. O,O

-> is the ghost of heisenberg behind this (energy defined always as part of an interval)?

2) at equilibrium, I expect S to be at its maximum. so dS/dE should be equal to 0! and 1/0, well...

I'm very curious to see ideas about this!

Thanks for any ideas!