Cosmology, Decoherence and the Second Law

TL;DR

The paper investigates the quantum thermodynamics of the early universe by contrasting a simple discrete system–environment model with a continuum cosmological setup, using open EFT methods to compute entanglement entropy of inflationary fluctuations. It shows that in the discrete case, entropy growth tracks the decay of the environmental overlap $|r(t)|$, while in quasi-de Sitter cosmology the off-diagonal density-matrix elements in the field basis need not decay outright, yet the entanglement entropy of soft modes increases monotonically during periods of acceleration ($\ddot{a}>0$) due to both fixed-cutoff Lindblad-type evolution and a diffusion term from the time-dependent horizon cutoff $\Lambda(t)=\varepsilon aH$. The analysis covers Gaussian states and extends to non-Gaussian cases, clarifying the relationship between von Neumann entropy and thermodynamic entropy in cosmology and showing how horizon dynamics can drive an arrow of time without requiring a complete thermalization of the universe. Overall, the work provides a concrete framework for understanding entropy production via entanglement in expanding spacetimes and highlights the distinctions between microscopic quantum entropy and the cosmological thermodynamic entropy budget.

Abstract

We consider quantum decoherence and entropy increase in early universe cosmology. We first study decoherence in a discrete bipartite quantum system for which a single qubit gets entangled with an environment and the entropy increase is correlated with the decay of the off-diagonal terms of the reduced density matrix. We compare this system with continuous systems relevant for cosmology for which there is a natural external intervention, corresponding to the time-dependent separation between the sub- and super-horizon inflationary fluctuations. We find, in this case, that the off-diagonal terms of the density matrix, in a field basis, do not decay as sometimes assumed in cosmological set-ups. Nevertheless, following a recent treatment in terms of open Effective Field Theories (EFTs), we compute the entanglement entropy for a Gaussian state and show that it actually increases monotonically ($\dot S>0$) during the accelerated phases ($\ddot a>0$ with $a(t)$ the scale factor). We generalise this result to include non-Gaussian states and briefly discuss the relevance of computing the von Neumann entropy as compared to the thermodynamic entropy.