https://hackerpaper.kaipfister.de/p/2307.11372/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=46920971urn:hackerpapers:mention:2307.11372:46920971Sat, 07 Feb 2026 03:15:27 GMT<p>More specifically, dice-inspired (positive integer-related) probability distributions https://arxiv.org/abs/2307.11372 tilt maps [on dice polynomials].. that are measure-class-preserving and commute with convolution. as an alternative to max entropy to derive Boltzmann law for &quot;the ideal free market&quot;</p><p><a href="https://hackerpaper.kaipfister.de/p/2307.11372/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.PRhttps://news.ycombinator.com/item?id=46907016urn:hackerpapers:mention:2307.11372:46907016Thu, 05 Feb 2026 23:36:58 GMT<p>Original article: &quot;On the origin of the Boltzmann distribution&quot; - https://arxiv.org/abs/2307.11372 Abstract: &quot;Boltzmann distributions are used in statistical mechanics to describe how the states of a system are distributed at a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of…</p><p><a href="https://hackerpaper.kaipfister.de/p/2307.11372/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.PR