Answer to Question #96302 in Physics for saurav

Question

how does the thermodynamic probability differ from mathematical probability

Answer 1

Thermodynamic probability is defined as the number of alternative microscopic arrangements which correspond to the same macroscopic state. 

Mathematical probability is the ratio of the number of favorable events to the number of equally possible events.

In general, probability is proportional to multiplicity and the proportionality factor can be constant or some function (here of energy). The two cannot be the same because probabilities are numbers between 0 and 1 and multiplicities are integers larger than or equal to 1.