GITAM, Department of Engineering Physics
Entropy and probability
In 1896 Boltzmann discovered a relation between entropy and probability. Boltzmann stated from a simple idea that the equilibrium state of the system is the state of maximum probability, ie., the probability of the system in equilibrium state is maximum. But from the thermo dynamical point of view the equilibrium state of the system is the state of maximum entropy. If the system is not in equilibrium, then changes takes place within the system until the equilibrium state or the state of maximum entropy is reached. Thus in the equilibrium state both the entropy and thermo dynamical probability have the maximum values which led Boltzmann to expect the co-relation between them.
According to Boltzmann, the relation between entropy and probability is
S = k lnW
Where S is the entropy, k is Boltzmann constant and W is the probability of the state