A thermodynamic origin for the Cohen-Kaplan-Nelson bound

Department of Physics & Astronomy, Rutgers, The State University of New Jersey - 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA

^(a) ramakrishna@physics.rutgers.edu (corresponding author)

Received: 14 November 2021
Accepted: 10 January 2022

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 possible solution to this extremization problem (with ), 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.