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.[1][2] The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the "mixing paradox". If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, in the thermodynamic limit, the paradox is averted.
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leads to a paradox known as the Gibbsparadox, after Josiah Willard Gibbs, who proposed this thought experiment in 1874‒1875. The paradox allows for the...
cell is found do we ask which kind of molecule is there. See also: Gibbsparadox, in which it would seem that "mixing" two samples of the same gas would...
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list...
Ben-Naim, Arieh (21 September 2007). "On the So-Called GibbsParadox, and on the Real Paradox" (PDF). Entropy. 9 (3): 132–136. Bibcode:2007Entrp...9....
there exists a set of physical paradoxes that directly rely on one or more assumptions that are incorrect. The Gibbsparadox of statistical mechanics yields...
History, a Theory, a Flood. New York, NY: Pantheon. Lin, Shu-Kun (2008). "GibbsParadox and the Concepts of Information, Symmetry, Similarity and Their Relationship"...
the numbers of each type of indistinguishable particle to avoid the Gibbsparadox. Quantum physics provides the underlying reason for why these corrections...
strongly implies the violation of the second law of thermodynamics. See Gibbsparadox. Uncertainty principles relate quantum particles–electrons for example–to...
When combined with thermodynamics, classical mechanics leads to the Gibbsparadox of classical statistical mechanics, in which entropy is not a well-defined...
using Gibbs free energy of mixing Δ G m i x = Δ H m i x − T Δ S m i x {\displaystyle \Delta G_{mix}=\Delta H_{mix}-T\Delta S_{mix}} However, Gibbs free...
non-extensive entropy in the canonical ensemble, known today as the Gibbsparadox. In the grand canonical ensemble a further logical inconsistency occurs:...
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol G {\displaystyle G} ) is a thermodynamic potential that can...
volume of states of fixed radius r {\displaystyle r} (as described in Gibbsparadox).[clarification needed] A solution of this form can be plugged into...
indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox. There are two methods for distinguishing between particles. The...
combined with classical thermodynamics, classical mechanics leads to the Gibbsparadox in which entropy is not a well-defined quantity. As experiments reached...
systems, such as the ultraviolet catastrophe in black-body radiation, the Gibbsparadox, and the lack of a zero point for entropy. Since classical physics corresponds...
computer simulation demonstrating Savant's predicted result. The problem is a paradox of the veridical type, because the solution is so counterintuitive it can...
measure—dimensionality—of subspace of Hilbert space), and applied this to the Gibbsparadox. Saunders has also developed a general framework for the treatment of...
{\displaystyle g_{l}} represent the Gibbs free energy of a molecule in the vapor and liquid phase respectively. The change in the Gibbs free energy is then: Δ G...
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