On the Second Law of Thermodynamics: The Significance of Coarse-Graining and the Role of Decoherence

TL;DR

This paper explores how coarse-graining and decoherence influence the interpretation of the second law of thermodynamics, particularly regarding the universe's low initial entropy and the thermodynamic arrow of time.

Contribution

It analyzes the role of decoherence in selecting coarse-graining methods and how this affects entropy calculation and the initial low entropy condition.

Findings

Decoherence constrains the coarse-graining process.

Coarse-graining can reverse entropy increase.

Low initial entropy imposes constraints on decoherence.

Abstract

We take up the question why the initial entropy in the universe was small, in the context of evolution of the entropy of a classical system. We note that coarse-graining is a an important aspect of entropy evaluation which can reverse the direction of the increase in entropy, i.e., the direction of thermodynamic arrow of time. Then we investigate the role of decoherence in the selection of coarse-graining and explain how to compute entropy for a decohered classical system. Finally, we argue that the requirement of low initial entropy imposes constraints on the decoherence process.