D. Koutsoyiannis, Physics of uncertainty, the Gibbs paradox and indistinguishable particles, *Studies in History and Philosophy of Modern Physics*, 44, 480–489, doi:10.1016/j.shpsb.2013.08.007, 2013.

[doc_id=1381]

[English]

The idea that, in the microscopic world, particles are indistinguishable, interchangeable and without identity has been central in quantum physics. The same idea has been enrolled in statistical thermodynamics even in a classical framework of analysis to make theoretical results agree with experience. In thermodynamics of gases, this hypothesis is associated with several problems, logical and technical. For this case, an alternative theoretical framework is provided, replacing the indistinguishability hypothesis with standard probability and statistics. In this framework, entropy is a probabilistic notion applied to thermodynamic systems and is not extensive per se. Rather, the extensive entropy used in thermodynamics is the difference of two probabilistic entropies. According to this simple view, no paradoxical behaviours, such as the Gibbs paradox, appear. Such a simple probabilistic view within a classical physical framework, in which entropy is none other than uncertainty applicable irrespective of particle size, enables generalization of mathematical descriptions of processes across any type and scale of systems ruled by uncertainty.

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**Additional material:**

- Preprint (668 KB)
- Prehistory: rejections by 7 journals (1097 KB)

**See also:**
http://dx.doi.org/10.1016/j.shpsb.2013.08.007

**Our works referenced by this work:**

1. | D. Koutsoyiannis, Uncertainty, entropy, scaling and hydrological stochastics, 1, Marginal distributional properties of hydrological processes and state scaling, Hydrological Sciences Journal, 50 (3), 381–404, doi:10.1623/hysj.50.3.381.65031, 2005. |

2. | D. Koutsoyiannis, An entropic-stochastic representation of rainfall intermittency: The origin of clustering and persistence, Water Resources Research, 42 (1), W01401, doi:10.1029/2005WR004175, 2006. |

3. | D. Koutsoyiannis, Hurst-Kolmogorov dynamics as a result of extremal entropy production, Physica A: Statistical Mechanics and its Applications, 390 (8), 1424–1432, doi:10.1016/j.physa.2010.12.035, 2011. |

4. | D. Koutsoyiannis, A hymn to entropy (Invited talk), IUGG 2011, Melbourne, doi:10.13140/RG.2.2.36607.61601, International Union of Geodesy and Geophysics, 2011. |

**Our works that reference this work:**

1. | D. Koutsoyiannis, Entropy: from thermodynamics to hydrology, Entropy, 16 (3), 1287–1314, doi:10.3390/e16031287, 2014. |

2. | D. Koutsoyiannis, Entropy production in stochastics, Entropy, 19 (11), 581, doi:10.3390/e19110581, 2017. |

3. | D. Koutsoyiannis, and G.-F. Sargentis, Entropy and wealth, Entropy, 23 (10), 1356, doi:10.3390/e23101356, 2021. |

4. | D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023. |

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**Tagged under:**
Determinism vs. stochasticity,
Entropy,
Papers initially rejected,
Uncertainty