In physics, the ground state of a quantum mechanical system is its lowest-energy state. An excited state is any state with energy greater than the ground state.
If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states, for example, the hydrogen atom. It turns out that degeneracy occurs whenever a nontrivial unitary operator commutes with the Hamiltonian of the system.
According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as crystal lattices, have a unique ground state and therefore have zero entropy at absolute zero (because ln(1) = 0).
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