Consider a collection of N two level systems in thermal equilibrium at a temperature T. Each system has only two states, a ground state of energy 0 and an excited state of energy ϵ. The probability that a system will be found in excited state and entropy respectively at very high temperature, are

1
P → 0, S → 0
2
→ 1/2, S → Nk ln 2
3
P → ∞, S → ∞
4
P → 1/2, S → Nk ln 3

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