PPT Slide
Fundamental assumption: an isolated system (N, V and U and all external parameters constant) is equally likely to be in any of the quantum states accessible to it!
A quantum state is accessible if its properties are compatible with the physical specification of the system
Probability of a state s: P(s). Let g be the number of accessible states -->
P(s)=1/g if the state s is accessible, and P(s)=0 otherwise
Ensemble: a collection of many “copies” (replica) of the original system. If there are g accessible states there are g replicas, one in each accessible quantum state. Averages calculated by us are all ensemble averages
Ergodic hypothesis: the thermodynamic systems goes over all accessible states in a very short time (in a time much shorter than needed for the measurement of a macroscopic parameter)
Basic hypothesis for an isolated system: time average equals the ensemble average
Example: Ensemble of a system of 10 spins with energy -8mB and spin exces 2s=8.