A thermodynamic origin for the Cohen-Kaplan-Nelson bound

TL;DR

This paper derives the Cohen-Kaplan-Nelson bound from a thermodynamic perspective, showing it as a natural consequence of extremizing the universe's free energy with respect to the Hubble radius, and explores alternative solutions.

Contribution

It introduces a thermodynamic framework for understanding the CKN bound without relying on density of states or minimal coupling assumptions, linking holography and cosmology.

Findings

CKN bound emerges as a solution to a free energy extremization problem

Alternative solutions with different entropy scaling exponents are possible

Holographic principle aligns with free energy minimization in cosmology

Abstract

The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. We do so by defining an appropriate Helmholtz free energy which when extremized relative to a key parameter (the Hubble radius L) provides a scaling formula for the entropy with the Hubble radius (an exponent 'r' used in the text). We deduce that the CKN bound is one solution to this extremization problem (with r=3/2), but there are others consistent with r=2. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.