The classic laws of thermodynamics might be wrong for finite systems like small clusters of atoms or tiny biological structures.
March 31, 2026
Original Paper
Trinity of Varentropy: Finiteness, Fluctuations, and Stability in Power-Law Statistics
arXiv · 2603.27997
The Takeaway
For over a century, physics has assumed the environment is 'infinitely large,' but real-world systems are often small and limited. By introducing a concept called 'Varentropy,' researchers have created a new framework that explains why these smaller systems follow 'power-law' patterns that traditional thermodynamics simply couldn't account for.
From the abstract
Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the \textit{renormalized entropy} $s_{2-q}$. Derived from the asymptotic scaling of the combinatorial $q$-factorial, this quantity yields a stable thermodynamic limit, remaining finite ($O(N^0)$) for systems with strong correlations. Furthermore, we clarify the physic