Extensive Entropy Bounds

TL;DR

This paper explores how entropy bounds like Bekenstein and holographic bounds lead to new insights in systems with extensive entropy, connecting black hole physics, thermodynamics, and quantum field limits.

Contribution

It demonstrates that entropy bounds imply specific limits on radiation entropy, relate black hole physics to thermodynamics, and constrain the number of massless field species.

Findings

Bekenstein bound yields the Unruh-Wald entropy bound.

Spherical entropy bound implies the causal entropy bound.

Number of massless field species is limited to about 10^4.

Abstract

It is shown that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. More explicitly, the Bekenstein entropy bound leads to the entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy bound implies the "causal entropy bound". Surprisingly, the first bound shows a close relationship between black hole physics and the Stephan-Boltzmann law (for the energy and entropy flux densities of the radiation emitted by a hot blackbody). Furthermore, we find that the number of different species of massless fields is bounded by $\sim 10^{4}$.