Entropy

Gibbs paradox

In statistical mechanics, a semi-classical derivation of entropy that does not take into account the indistinguishability of particles yields an expression for entropy which is not extensive (is not proportional to the amount of substance in question). This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs, who proposed this thought experiment in 1874‒1875. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the "". If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, the paradox is averted. (Wikipedia).

Gibbs paradox
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Related pages

Line integral | Boltzmann's entropy formula | Hamiltonian mechanics | Identical particles | Momentum | Stirling's approximation | Phase space | Entropy | Point (geometry) | Gamma function | Fermi–Pasta–Ulam–Tsingou problem | N-sphere | Particle number | Sackur–Tetrode equation | Liouville's theorem (Hamiltonian) | Second law of thermodynamics | Josiah Willard Gibbs | Circle | Combination | Ergodic hypothesis