Ginestra Bianconi and John Onimisi Obidi on Gravity, Spacetime

Ginestra Bianconi's Gravity from Entropy (GfE) and John Onimisi Obidi's Theory of Entropicity (ToE): Modern Insights on Gravity, Matter, Energy, and Spacetime

1. Introduction

The Theory of Entropicity (ToE) is a proposed unifying framework in theoretical physics that treats entropy as the fundamental organizing principle of spacetime, gravity, and cosmic structure. Within this perspective, gravitational dynamics, dark energy, and the emergence of complexity are understood as manifestations of entropic processes rather than purely geometric or force-based phenomena.

A recent development in quantum gravity, known as Gravity from Entropy (GfE), introduced by Professor Ginestra Bianconi (Queen Mary University of London), provides a thermodynamic formulation of gravity based on Quantum Geometric Relative Entropy (QGRE). While GfE is a self-contained theory, its conceptual structure fits naturally under the broader umbrella of the Theory of Entropicity. ToE generalizes and extends the ideas of GfE by elevating entropy from a derived quantity to a fundamental field.

This article presents an encyclopedic overview of the relationship between ToE and GfE, emphasizing how ToE provides a comprehensive umbrella framework for thermodynamic and informational approaches to gravity and cosmology.

2. Background: Entropy and Cosmic Structure

The **second law of thermodynamics** states that the total entropy of an isolated system tends to increase over time. Applied to cosmology, this implies that the universe, treated as an approximately isolated system, must evolve toward states of higher total entropy. This raises a longstanding conceptual problem: the universe exhibits increasing **structure and complexity** over time, including the formation of galaxies, stars, planets, and biological systems, which appear locally ordered.

The tension between global entropy increase and local order has motivated a variety of approaches in statistical mechanics, cosmology, and quantum gravity. The Theory of Entropicity and Gravity from Entropy both address this tension by interpreting gravitational and cosmological dynamics as thermodynamic phenomena.

3. Gravity from Entropy (GfE)

3.1 Conceptual Foundations

Gravity from Entropy (GfE) is a quantum gravity framework that derives gravitational dynamics from the microscopic degrees of freedom of spacetime geometry using principles of statistical mechanics and information theory. The central object in GfE is the Quantum Geometric Relative Entropy (QGRE), which quantifies the informational tension between:

• the physical spacetime metric, and
• the metric induced by matter fields and curvature.

In GfE, the gravitational Lagrangian is constructed from QGRE. This leads to field equations that reduce to general relativity in the low-energy, weak-curvature limit, but deviate from it at higher energies or stronger curvature regimes.

4. Thermodynamic Structure

In Friedmann–Robertson–Walker (FRW) cosmological spacetimes, GfE exhibits a rich thermodynamic structure. The local geometric degrees of freedom satisfy a relation analogous to the first law of thermodynamics, in which:

• an emergent dynamical dark energy term plays the role of internal energy,
• QGRE can be interpreted as local entropy per unit volume,
• effective **temperature** and **pressure** arise naturally from the underlying quantum state of spacetime.

This suggests that spacetime, in the GfE framework, possesses an intrinsic thermal nature.

5. Entropy Density and Total Entropy

A key result of GfE is the distinction between total entropy and entropy density. As the universe expands, the local volume element associated with the physical metric increases. Within GfE:

• the total entropy of the universe increases over time, consistent with the second law of thermodynamics;
• the entropy per unit volume (local QGRE density) decreases over time.

This dual behavior provides a thermodynamic explanation for the emergence of local structures: global entropy increases, while local entropy density decreases, allowing ordered structures to form without violating the second law.

6. Dark Energy and Deviations from General Relativity

Beyond the weak-field limit, the GfE equations deviate from general relativity and include an emergent dynamical dark energy term. This term can be interpreted thermodynamically as internal energy associated with the geometric degrees of freedom. The presence of such a term suggests potential observational consequences and testable predictions, particularly in cosmology.

7. Theory of Entropicity (ToE)

7.1 Entropy as Fundamental Field

The Theory of Entropicity (ToE) generalizes the thermodynamic and informational insights of GfE by treating entropy not merely as a measure of geometric tension but as a fundamental physical field. In ToE, spacetime geometry, curvature, and gravitational dynamics are emergent phenomena arising from the configuration and evolution of an underlying Entropic Field.

Rather than starting from a pre-given metric and then defining entropy on top of it, ToE posits that metric structure itself is a macroscopic manifestation of entropic relations. This shifts the conceptual hierarchy: entropy is primary, geometry is secondary.

7.2 Spectral Obidi Action

At the core of ToE is a variational principle known as the Spectral Obidi Action. This Action is constructed from quantities that encode the entropic curvature of spacetime. In broad terms, the Spectral Obidi Action is designed such that:

• global entropy is extremized (typically maximized) subject to constraints;
• local entropy density is minimized in regions where structure forms;
• gravitational field equations emerge as the Euler–Lagrange equations of an entropic functional.

This dual extremization principle provides a natural mechanism for reconciling global entropy increase with local order: the universe evolves toward states of higher total entropy while simultaneously redistributing entropy in such a way that local entropy density can decrease, enabling structure formation.

7.3 Global Second Law and Local First Law

ToE explicitly distinguishes between:

• the global second law of thermodynamics, which governs the overall evolution of the universe and ensures that total entropy increases;
• local first-law-like identities, which govern the thermodynamic behavior of spacetime regions and relate internal energy, entropy, temperature, and pressure.

In this sense, ToE incorporates both the second law (as a global constraint) and first-law relations (as local dynamical identities), mirroring and extending the thermodynamic structure observed in GfE.

7.4 Dark Energy as Entropic Potential Within ToE, dark energy is interpreted as an entropic potential associated with the Entropic Field. Rather than being an ad hoc cosmological constant or an unexplained fluid, dark energy arises naturally as a global entropic contribution to the Action. This aligns with the GfE interpretation of dark energy as internal energy, but embeds it in a more general entropic framework.

8. Relationship Between GfE and ToE

8.1 Conceptual Integration

Gravity from Entropy (GfE) and the Theory of Entropicity (ToE) share a common philosophical and mathematical foundation: both treat gravity as fundamentally thermodynamic and informational. However, their roles are different in scope.

GfE can be viewed as a specific realization of entropic gravity in which:

• gravity is derived from relative entropy between two metrics;
• thermodynamic identities emerge in FRW cosmology;
• dark energy appears as internal energy;
• entropy density and total entropy exhibit distinct behaviors.

ToE, by contrast, is an umbrella framework that:

• promotes entropy to a fundamental field;
• treats geometry as emergent from entropic relations;
• introduces the Spectral Obidi Action as a unique entropic variational principle;
• unifies global and local thermodynamic laws;
• provides a systematic explanation for the emergence of complexity and structure.

In this sense, GfE fits naturally under ToE as a thermodynamic sub-theory or special case, particularly in cosmological settings.

8.2 Comparative Summary

In GfE, entropy is primarily a relative measure between metrics (QGRE), and gravity emerges from this informational tension. In ToE, entropy is the origin of metric structure itself, and gravity is the macroscopic manifestation of entropic curvature.

GfE demonstrates that spacetime patches obey a first-law-like thermodynamic relation and that total entropy increases while entropy density decreases. ToE explains these features as consequences of a deeper entropic extremization principle encoded in the Spectral Obidi Action.

Dark energy in GfE is an emergent internal energy term. In ToE, dark energy is a global entropic potential, arising from the configuration of the Entropic Field.

9. Significance for Modern Theoretical Physics

The integration of GfE within the Theory of Entropicity reflects a broader paradigm shift in theoretical physics: gravity, spacetime, and cosmic complexity are increasingly understood as thermodynamic and informational phenomena rather than purely geometric constructs.

This shift has several implications:

• It strengthens the conceptual bridge between general relativity, quantum mechanics, thermodynamics, and information theory.
• It offers new perspectives on cosmological irreversibility, the arrow of time, and the foundations of complexity.
• It suggests that dark energy and structure formation may be understood within a unified entropic framework, potentially guiding future observational and theoretical work.

By providing an umbrella structure that encompasses GfE and related approaches, the Theory of Entropicity aims to offer a coherent, mathematically grounded, and conceptually unified description of gravity and cosmology.

10. Publication Reference

The key modern reference for Gravity from Entropy is:

• Ginestra Bianconi, Thermodynamics of the Gravity from Entropy Theory, Physical Review D (2024-2025).

The Theory of Entropicity is an ongoing theoretical program, with foundational work focusing on the formulation of the Spectral Obidi Action and the entropic interpretation of spacetime geometry.

11. See Also

• Entropic gravity
• Thermodynamics of spacetime
• Information geometry
• Quantum gravity
• Dark energy in cosmology

For Details: 📚Reference(s): The Canonical Archives: https://entropicity.github.io/Theory-of-Entropicity-ToE/

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