Gravity from Entropy Theory Derives Thermodynamics for Friedmann Universes Via, Temperature And, Pressure

The fundamental nature of gravity remains a central question in physics, and recent work explores the possibility that gravity arises from underlying principles of entropy. Ginestra Bianconi from Queen Mary University of London, along with colleagues, investigates this concept through a thermodynamic framework, deriving the Hamiltonian associated with a theory known as Gravity from Entropy. This research reveals a connection between the geometry of spacetime and thermodynamic quantities like temperature and pressure, demonstrating that Friedmann universes, which describe the expansion of the cosmos, possess properties linked to their local energy and a measure called Geometric Relative Entropy. By establishing a thermodynamic consistency for these universes, the team demonstrates that while geometric relative entropy may not always increase, the overall entropy of an expanding universe does not decrease, offering new insights into the statistical mechanics of gravity and its implications for cosmology.

This research derives a mathematical description, the Hamiltonian, for isotropic spacetimes, defining the system’s energy and behavior using the tools of statistical mechanics. The analysis reveals that spacetime possesses a k-temperature and k-pressure, quantities linked to the geometric properties of space and time, and dependent on whether those properties are spatial or temporal in nature.

Spacetime Thermodynamics and Emergent Cosmology

Scientists have established a thermodynamic framework for a novel theory of gravity, where gravity arises from statistical mechanics and information theory. This work derives the Hamiltonian associated with the theory for isotropic spacetimes, defining both the Lagrangian and Hamiltonian using a purely statistical mechanics approach. The research reveals that spacetime is associated with a k-temperature and k-pressure, dependent on the order of the geometric degrees of freedom considered, demonstrating a distinct temperature and pressure for scalar, vector, and bivector degrees of freedom. Measurements confirm that the energy per unit volume coincides with the emergent cosmological constant predicted by the theory, consistently remaining positive.

These thermodynamic quantities are interconnected by the first law of thermodynamics, establishing a fundamental relationship between energy, temperature, and pressure within this framework. This divergence leads to a scaling of total entropy with time for Friedmann universes, while the total energy remains constant for universes dominated by radiation or matter. Further analysis of de Sitter space reveals that the total entropy associated with a de Sitter space causal diamond scales as the inverse square of the Hubble constant, H−2, for small values of H. The theory posits a true topological metric, ̃g, distinct from the metric induced by matter and curvature, ̃G, and the research demonstrates how these metrics contribute to the emergent thermodynamic properties of spacetime.

Entropy and Thermodynamics of Expanding Universes

This work establishes a thermodynamic framework for the Gravity from Entropy (GfE) theory, revealing connections between spacetime geometry and fundamental thermodynamic properties. By applying statistical mechanics to isotropic spacetimes, specifically Friedmann-Robertson-Walker (FRW) universes, researchers derived a Hamiltonian and demonstrated that metric degrees of freedom are associated with temperature and pressure, dependent on their spatial or temporal nature. The analysis confirms adherence to the first law of thermodynamics within this GfE framework. These findings provide a comprehensive thermodynamic interpretation of the GfE theory, potentially offering new insights into classical and quantum gravity, statistical mechanics, entanglement theory, and cosmology.

Entropy and Emergent Gravity Framework Detailed

This research proposes a framework for understanding gravity and cosmology based on the idea that gravity emerges from entropy, viewing spacetime not as a smooth entity but as a complex statistical system. The fundamental premise is that the geometry of spacetime is linked to entropy, and changes in geometry correspond to changes in entropy. The research introduces the concepts of k-temperature and k-pressure associated with the metric, quantities that describe the thermodynamic state of spacetime itself, dependent on the order and type of the metric’s degrees of freedom. The framework is designed to satisfy the first law of thermodynamics, relating changes in spacetime’s energy to changes in its entropy and other thermodynamic variables.

Applying this framework to cosmology, scientists aim to derive the Friedmann equations, which describe the expansion of the universe, from thermodynamic principles. The work also connects to quantum information theory, suggesting that entanglement plays a crucial role in the emergence of spacetime. If this framework proves correct, it could profoundly change our understanding of gravity, potentially revealing it not as a fundamental force but as an emergent phenomenon. It could also shed light on the initial conditions of the universe, the thermodynamics of black holes, and the nature of dark energy and dark matter. This framework could also provide a new approach to developing a theory of quantum gravity.