Entropy Gravity Theory Provides New Clues to Reconcile Gravity With Thermodynamics’ Second Law

A new theoretical study from Queen Mary University of London examines a problem at the heart of cosmology: how the Universe can become more structured and complex over time without violating the second law of thermodynamics. The second law, often summarized as entropy tending to increase in isolated systems, appears to predict a march toward greater disorder—yet the cosmos clearly does the opposite in many respects, building galaxies, stars, planets, and eventually life.

In the work, Professor Ginestra Bianconi approaches the tension using Gravity from Entropy (GfE), a quantum-gravity framework that treats gravity as emerging from microscopic statistical properties of spacetime. Rather than taking spacetime geometry as merely a stage on which physics happens, GfE links geometric dynamics to entropy-like quantities defined through information-theoretic measures.

At the mathematical core of the theory is the Quantum Geometric Relative Entropy (QGRE), constructed as an entropy measure between the “true” spacetime metric and a metric induced by matter fields and curvature. In low-energy and weak-curvature regimes, the resulting field equations reproduce General Relativity, ensuring compatibility with known gravitational physics. However, when one moves beyond that limit, the theory departs from Einstein’s equations and naturally allows a dynamical dark-energy contribution.

The paper studies these ideas in Friedmann–Robertson–Walker cosmologies, the standard description of an expanding, homogeneous, and isotropic universe. The authors show that the local geometric degrees of freedom satisfy a form of the first law of thermodynamics, with the emergent dark-energy term behaving like an internal energy contribution.

A key result concerns how entropy is tracked. While the total entropy of the Universe increases as the cosmos expands, the entropy per unit volume—identified with the local QGRE—decreases over time. This distinct behavior provides a new lens for thinking about how localized complexity can arise even as global thermodynamic irreversibility continues.

The analysis also highlights the role of the physical volume element determined by the metric measure. As the Universe expands, that volume grows, helping explain why total entropy rises even while the local entropy density falls. Effective temperature and pressure quantities emerge consistently within the GfE thermodynamic picture.

Although still early and theoretical, the study suggests that gravity and spacetime may possess an intrinsic informational and thermal character. By offering a route to reconcile thermodynamic irreversibility with the emergence of structured cosmic outcomes, it could help connect general relativity, thermodynamics, quantum theory, and cosmology.

Overall, the findings motivate further exploration of how an entropic origin of gravity can address deep questions about complexity—potentially reaching all the way to the conditions that make life possible.