Testing the Quantum of Entropy

TL;DR

This paper reviews the concept of a quantum of entropy, clarifies its limits, and discusses its implications for thermodynamics, black hole entropy, and fundamental physical principles.

Contribution

It provides a comprehensive analysis of entropy limits, resolving conceptual tensions and proposing a universal principle of the entropy quantum based on the Boltzmann constant.

Findings

Entropy has a lower bound of S ≥ k ln 2.

The quantum of entropy is given by the Boltzmann constant k.

Vanishing entropy claims contradict observability and the entropy quantum.

Abstract

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a lower entropy limit $S \geq k \ln 2$. Conceptual tensions with the third law of thermodynamics and the additivity of entropy are resolved. Black hole entropy is also surveyed. Further claims for vanishing entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time, also implies $S \geq k \ln 2$. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of a quantum of entropy enable one to speak about a principle of the entropy limit that is valid across nature.