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Summary:

I was studying statistical mechanics when I came to know about the Boltzmann's entropy relation, ##S = k_B\ln Ω##.
What does 'thermodynamic probability' actually mean and how does it give rise to the Entropy?
Main Question or Discussion Point
I was studying statistical mechanics when I came to know about the Boltzmann's entropy relation, ##S = k_B\ln Ω##.
The book mentions ##Ω## as the 'thermodynamic probability'. But, even after reading, I can't understand what it means. I know that in a set of ##Ω_0## different accessible states, an isolated system has a probability ##P = \frac 1 {Ω_0}## of being in any one of the state and that at equilibrium when entropy is maximum, the probability of the system being in various accessible states do not vary with time. Also, when two interacting systems are in equilibrium, the no of states available to the combines system is maximum.
In the Boltzmann's entropy relation, ##S = k_B\ln Ω##, what does the ##Ω## signify? If it is a probability what is it the probability of and for which system are we getting the Entropy?
The book mentions ##Ω## as the 'thermodynamic probability'. But, even after reading, I can't understand what it means. I know that in a set of ##Ω_0## different accessible states, an isolated system has a probability ##P = \frac 1 {Ω_0}## of being in any one of the state and that at equilibrium when entropy is maximum, the probability of the system being in various accessible states do not vary with time. Also, when two interacting systems are in equilibrium, the no of states available to the combines system is maximum.
In the Boltzmann's entropy relation, ##S = k_B\ln Ω##, what does the ##Ω## signify? If it is a probability what is it the probability of and for which system are we getting the Entropy?