How does the Theory of Entropicity (ToE) derive gravity and spacetime from entropy?

In ToE, gravity is described as an **emergent effect of entropy gradients**, not as a fundamental force or merely as spacetime curvature. The theory’s public descriptions say that entropy is promoted to a dynamical field $$S(x)$$, and that motion, gravitation, and time arise from the constraints and gradients of that field [2].

## Core idea

The basic claim is that the **Obidi Action** treats entropy as the starting variable, and variation of that action yields the theory’s dynamical equations, including the **Master Entropic Equation**, entropic geodesics, and an entropy potential equation [2]. In that framing, gravity appears when matter and geometry respond to differences in entropy, so gravitational attraction is an emergent consequence of entropic structure rather than a separate fundamental interaction [1][2].

## Spacetime emergence

ToE also says spacetime itself is not primary. Instead, it is said to emerge from a deeper entropic manifold, with geometric structure linked to information metrics such as Fisher–Rao and Fubini–Study, plus the Amari–Čencov $$\alpha$$-connection formalism [2]. In that picture, spacetime geometry is the macroscopic limit of entropic ordering, and Einstein’s equations are presented as a limiting case [2].

## How the derivation is presented

One of the published ToE derivation is that higher-order entropy corrections to Newton’s gravitational potential, combined with inputs such as the Unruh effect, Hawking temperature, Bekenstein–Hawking entropy, the holographic principle, and orbital mechanics, can reproduce the perihelion shift of Mercury while interpreting gravity as entropy-driven [1]. So the theory’s derivation strategy is: start from entropy, build a variational principle, recover gravity and relativistic effects, then interpret spacetime as emergent from the same entropic substrate [1][2].