Negative temperature. 3 a system of n atoms each can be in the ground state or in an excited state. for convenience, we set the zero of energy exactly in between, so the energies of the two states of an atom are ±c/2. the atoms are isolated from the outside world. there are only weak couplings between the atoms, sufficient to bring them into internal equilibrium but without other effects. (a) microcanonical e (corresponding to a number of ercited atoms mee + n/2), what is the microcanon- cal entropy smicro(e) of our system? sim- plify your expression using stirling's formula, log n! n log n n. (b) negative temperature. find the temperature using your simplified erpression from part (a) what happens to the temperature when e 0? having the energy e 0 is a kind of popula- tion inversion. population inversion is the driv- ing mechanism for lasers. for many quantities, the thermodynamic deriva- tives have natural interpretations when viewed as sums over states. it is easiest to see this in small systems.