Boltzmann Equation for Entropy:
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Since degeneracy is the number of ways to achieve a particular energy state and entropy is the likelihood that the system will be in a particular state, degeneracy (W) being at a maximum probably means that the number of ways to achieve a particular energy state is the highest.
To be at maximum entropy is to be at the “most random” state. That’s not the best wording but I think Dr. Lavelle’s example in class is helpful: if he opened a sealed beaker of argon gas in the lecture hall, it would diffuse and spread through the entire room until it was at maximum entropy.
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