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https://doi.org/10.31224/5595...
Article . 2025 . Peer-reviewed
License: CC BY
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Preprint . 2025
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Entropy ≠ Disorder

Authors: Oliver, James;

Entropy ≠ Disorder

Abstract

Boltzmann’s formula, S = kB ln(Ω), is not a measure of "disorder," but a tool for counting accessible configurations. This is seen when arranging cards: one card has one configuration (Ω = 1, S = 0), while a full deck has an astronomical number (Ω = 52!, S ≈ 156 kB). The formula quantifies the size of this possibility space. Common examples reinforce this: the entropy of a "messy room" or the anagrams LISTEN/SILENT depends entirely on the constraints of the description, not on subjective labels. By focusing on what Boltzmann’s formula actually calculates, this paper clarifies a persistent pedagogical confusion, showing that entropy measures the size of the explorable space defined by physical constraints. Contribution: This paper synthesizes established results from statistical mechanics to make Boltzmann’s definition of entropy explicit. The contribution is not new physics but a clarification of persistent pedagogical confusion, building on critiques by Styer (2019) and Lambert (2002). We argue that entropy measures the size of the accessible possibility space, a framework that would be falsified if systems with identical macroscopic constraints could have different entropies or if the formula S = kB ln(Ω) failed to match measured data.

Keywords

Entropy, Thermodynamics, Statistical mechanics, Thermodynamic engineering

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
hybrid