Question

Consider the Boltzmann-Gibbs principle, also known as the fundamental principle or postulate of statistical mechanics.

a) state that principle for a system that is classically described.

b) state that principle for a system that is quantumly described.

In both cases, be careful to mention the system conditions in which the principle is considered valid.

Answer 1

(A).unlike boltzman distribution which describes probabilistic outcome of whole system from a single atom to macroscopic system,boltzman gibbs distribution applies some restrictions on this probabilistic outcome.in the classical case it limits the space in a certain range,as wavefuntion of system gets definite shape in that region,but it allows the energy to take any range...means in classical this distribution restrict the shape of system but do not restrict the energy of system.

(B).in quantum this distribution restrict the probability distribution of energies of system,but do not restrict the wavefunction space.so the wavefunction shape is determined by other conditions like continuity,but energy of quantum system follows the boltzman gibbs distribution.