Gibbs Paradox

The Gibbs Paradox arises in statistical mechanics when considering the entropy of ideal gases. It suggests that mixing two identical gases seems to lead to an increase in entropy, which appears counterintuitive since the gases are indistinguishable. This paradox highlights that entropy and statistical behavior depend on how we count microstates (the specific arrangements of particles). The resolution to the paradox is recognizing that when particles are identical, we shouldn't double-count their states, which leads to a consistent understanding of mixing entropy and the second law of thermodynamics.