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Degeneracy refers to the number of ways of achieving a given energy state. Disorder refers to the organization of atoms and molecules. They are similar in the fact that when either degeneracy (Boltzmann equation) or disorder increases, entropy also increases. Although they are similar properties, they are not the same.
Disorder refers to the way that energy and matter tend to disperse. Degeneracy refers to the number of ways of achieving a given state. Degeneracy occurs if the energy is unable to stay in one state, represented by the W value. For example, the different microstates, which correspond to each arrangement of atoms in the state, contribute to the degeneracy of a substance. As the number of microstates increases, there are more ways for the atoms to orient themselves. With a higher number of possible states, there is more disorder, as there is a more diverse selection of microstates which the atoms could orient themselves as. The Boltzmann equation states that S = k*ln(W), therefore the two are directly related. Higher degeneracy increases disorder
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