A Bound on Equipartition of Energy

TL;DR

This paper introduces the concept of an equipartition of energy bound (EEB) in thermodynamics, proposing an upper limit to energy distribution among particles based on quantum and holographic principles.

Contribution

It presents a novel thermodynamic bound (EEB) derived from quantum theorems and holographic entropy limits, linking quantum bounds to classical thermodynamics.

Findings

Proposes an energy equipartition bound of approximately 4.93.

Links the EEB to quantum theorems and holographic entropy bounds.

Analyzes statistical mechanics distributions with power-law behavior.

Abstract

In this article we want to demonstrate that the time-scale constraints for a thermodynamic system imply the new concept of {\it equipartition of energy bound} (EEB) or, more generally, a thermodynamical bound for the {\it partition} of energy. We theorized and discussed the possibility to put an upper limit to the equipartition factor for a fluid of particles. This could be interpreted as a sort of transcription of the entropy bounds from quantum-holographic sector: the EEB number $\pi^{2}/2 = 4.93$, obtained from a comparison between the Margolus-Levitin quantum theorem and the TTT bound for relaxation times by Hod, seems like a special value for the thermodynamics of particle systems. This bound has been related to the idea of an extremal statistics and independently traced in a statistical mechanics framework, analyzing the mathematical behavior of the distributions which obey to a thermodynamical statistics with a power law greater than the planckian one.