Question

Explain why the Boltzmann factor of a microstate is not equal to the microstate's probability.

Answer 1

Z=∑s()e−E(s)kT.The exponential is called theBoltzmann factor, the normalization constantZis calledthepartition function,

and microstae probability isthe omega . we know s = k ln( omega)

clearly both are not equal

we note that the Boltzmann factor is an exponential. it come From the exponential relationship between multiplicity and entropy. We also see anew way to think about temperature in this exponential behavior:kTsets the energy scaleat which a given state has appreciable probability. As we shall see, states with energiesless thankTabove the ground state have significant probability, states with energies abovethe ground state greater thankThave a less significant probability. For this reasonkTissometimes called the thermal energy associated with temperatureT.