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Increasing degeneracy results in an increase in entropy of the system. This is shown by the Boltzmann equation: S=kB*ln(W), where w is the degeneracy and S is entropy. Therefore, an increase in w increases the value of S, which is entropy. This also makes sense because degeneracy is the number of ways of achieving a given energy state and entropy is the likelihood that the system will be in a particular state. So, if there are more ways for a system to achieve a certain energy state, then there is a greater likelihood that the system will be in that state.
The number of possible states for a system of given energy is called the degeneracy and it is denoted by g in the equation S=k ln (g). So when there is an increase in the degeneracy the energy level is higher versus when the degeneracy decreases, the energy level is lower.
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