where ΔS is the change in entropy, ΔQ is the heat added to the system, and T is the temperature.

ΔS = ΔQ / T

The Fermi-Dirac distribution describes the statistical behavior of fermions, such as electrons, in a system:

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PV = nRT

where Vf and Vi are the final and initial volumes of the system.

The Gibbs paradox arises when considering the entropy change of a system during a reversible process: