The Gravity from Entropy theory offers new clues for reconciling gravity with the second law of thermodynamics

A new study by Queen Mary University of London mathematician Professor Ginestra Bianconi proposes a new perspective on one of the deepest questions in modern physics: how can the Universe become increasingly structured and complex while still obeying the second law of thermodynamics? 

Einstein famously stated that “The second law of thermodynamics occupies a unique position among the laws of Nature,” reflecting his conviction that it is among the most fundamental principles of physics and unlikely to be overthrown. The second law states that the total entropy of an isolated system tends to increase over time, a principle often associated with the growth of disorder. 

This presents a long-standing puzzle in cosmology. The early Universe is generally believed to have existed in a low-entropy state and to evolve toward states of higher entropy. Yet over cosmic history, the Universe has also given rise to increasingly complex structures, including galaxies, stars, planets, and ultimately life itself. Reconciling the emergence of such ordered structures with the relentless increase of entropy remains an open challenge. 

In a recent paper published in Physical Review D, Professor Bianconi investigates this question within the framework of the Gravity from Entropy (GfE) theory, a quantum gravity approach that derives gravity from the microscopic degrees of freedom of spacetime geometry using principles of statistical mechanics.  

In this study, by exploring the thermodynamic properties of the Gravity from Entropy theory, she shows that while the total entropy of the Universe increases in time, the entropy per unit volume decreases in time, leaving open new interpretations for the emergence of local structures.  

The connection between gravity and thermodynamics has been known since the pioneering work of Jacob Bekenstein and Stephen Hawking in the 1970s, which established that black holes possess entropy and emit thermal radiation. These discoveries suggested a deep relationship between spacetime, information, and thermodynamics.  

Gravity from Entropy (GfE) proposes that gravity emerges from the information-theoretic tension between the true spacetime metric and the metric induced by matter fields and curvature. This new physical interpretation of gravity is reflected in the GfE Lagrangian, which is given by the Quantum Geometric Relative Entropy (QGRE) between these two metrics. The GfE gravity equations reduce to  General Relativity for low energies and small curvature, but beyond the weak limit, they deviate from it. Interestingly, beyond the weak limit, the GfE equations include the emergence of a dynamical dark energy term that could lead to testable predictions of the theory. 

This study explores the thermodynamic properties of the GfE theory in Friedmann–Robertson–Walker cosmological spacetimes. The results show that the local geometric degrees of freedom satisfy a first law of thermodynamics, in which the emergent dynamical dark-energy contribution can be interpreted as an internal energy, while the Quantum Geometric Relative Entropy (QGRE) can be identified as the local entropy per unit volume. Within this framework, effective temperature and pressure quantities also emerge naturally. Together, these findings suggest that the quantum state underlying the GfE theory may possess an intrinsic thermal nature. 

The study also highlights the fundamental role of the local volume element defined by the measure induced by the physical metric. As the Universe expands, this volume grows over time. Within the framework of the GfE theory, this expansion leads to an increase in the total entropy, while the local QGRE per unit volume decreases with time. This result reveals a distinctive thermodynamic behaviour of the GfE theory. 

Overall, this work proposes that gravity and spacetime may have an intrinsic thermodynamic and informational nature. This opens new possibilities for understanding the deep connections between gravity, quantum theory, and the emergence of complexity in the Universe. 

While still at an early theoretical stage, the authors say the work could help bridge long-standing gaps between general relativity, thermodynamics, quantum mechanics, and cosmology. Hence, “This work reveals how the Gravity from Entropy theory can tackle the challenging question to reconcile the second principle of thermodynamics with the emergence of complexity in our Universe. These results may open new avenues for investigating the long-standing problem of reconciling the foundations of cosmological irreversibility, the emergence of complex structures, and ultimately life, with fundamental gravitational dynamics” says Professor Bianconi.   

You can read the full paper in the APS Journal.