What the Theory of Entropicity (ToE) has Achieved: Why No Prior Researcher Declared Entropy as a Fundamental Field With Its Own Spectral Action

In standard physics, entropy is indeed treated as a derived, coarse-grained quantity. The Theory of Entropicity (ToE) is explicitly changing that assumption by promoting entropy to a fundamental scalar field with its own action and kinematics. There is no theorem that forbids this; the real test is whether the resulting field equations consistently reproduce known physics and make new, testable predictions. That is exactly what the Theory of Entropicity (ToE) is designed to do.

No one did it, not because it is known to be wrong, but because no previous framework could justify entropy as a dynamical, local, field-like quantity capable of supporting a full action principle and field equations.

Let us explain this step by step with precision.

1. What entropy meant historically (the core obstacle)

For over 150 years (from Clausius to modern thermodynamics), entropy was understood as:

A global or quasi-local state variable,

A statistical summary of many particles,

A derived quantity,

Not something that exists at each point in spacetime,

Not something that has its own kinetic terms, gradients, curvature couplings, or variation principles.

Because of this, entropy was never treated as something that propagates or has a spectral operator acting on it.

It simply wasn’t considered a “thing” that could:

vary independently,

obey a differential equation,

create curvature,

or serve as a fundamental degree of freedom.

Every previous theory assumed:

Entropy depends on the underlying microphysics — it is not itself the microphysical driver.

So entropy could not be a field under those assumptions.

2. Information theorists used entropy — but never as a field

Shannon, Jaynes, Caticha, Amari, Čencov, and information geometers treated entropy as:

a functional of probability distributions, not a spacetime field, and never as a dynamical object with a spectral action.

Even Caticha’s Entropic Dynamics treats entropy as an inference tool — not as a physical field generating curvature or equations of motion.

They use entropy to compute motion; they don’t claim entropy is the field that creates motion.

The distinction is vast.

3. Gravitational thermodynamics used entropy — but only as a boundary quantity

Jacobson, Verlinde, Padmanabhan, Bianchi–Myers, and all holographic thermodynamic gravity approaches used entropy as:

a horizon property,

a thermodynamic relation,

or a constraint.

But none promoted entropy to a universal field with its own Lagrangian, action, and field equations.

Why Didn't They Promote Entropy to a Universal Field?

Because entropy in those frameworks is:

geometric,

emergent,

not local,

not fundamental,

not capable of propagating,

not endowed with independent degrees of freedom.

So an "entropy field" was not even conceptually possible within their framework.

4. Spectral Action Frameworks (Connes–Chamseddine) exist — but never applied to entropy

Noncommutative geometry introduced spectral actions, but these actions operate on:

Dirac operators,

spectral triples,

noncommutative manifolds,

curvature invariants.

No one has ever formulated:

a spectral action whose primary dynamical variable is entropy.

Why No Researcher Formulated That?

Because entropy has never been understood as something with:

an operator algebra,

eigenmodes,

propagating quanta,

or spectral flow.

In other words:

Entropy has never been seen as something you can do spectral geometry on.

ToE is the first to bring the two worlds together:

Entropy → as a dynamic local field

Spectral operators → as the machinery determining its curvature and flow

Action principle → Obidi Action

Path integral → Vuli-Ndlela Integral

That unification did not exist before.

5. Why didn’t anyone else attempt what ToE has done?

Because it requires four conceptual leaps that no prior researcher made simultaneously:

(i) Entropy as a local field defined at every spacetime point

This contradicts the standard thermodynamic view of entropy as a global measure.

(ii) Entropy with its own kinetic terms (gradients, flow equations)

This transforms entropy into a dynamical object — unprecedented.

(iii) Entropy generating curvature and motion

This inverts the logic of GR and replaces metric curvature with entropy flow, which no one has proposed.

(iv) Entropy embedded in a spectral action with operators, eigenvalues, and functional traces

This is entirely new because entropy was never treated as a spectral object.

No previous framework had:

the mathematical courage,

the conceptual flexibility,

or the physical motivation

to make all four jumps at once.

ToE does.

6. So why did no one have the courage? Because:

A. They assumed entropy cannot be fundamental

Because it was always defined in terms of something else (microstates, horizon area, probabilities).

B. They assumed entropy cannot propagate

Because entropy production was seen as irreversible, not wave-like.

C. They assumed entropy cannot have curvature

Because curvature belonged to geometry, not thermodynamics.

D. They assumed entropy cannot have an action

Because action principles require variational fields, not statistical summaries.

E. They assumed spectral geometry is only for geometry, not thermodynamics

Because no one connected entropy to spectral triples before.

7. Does this mean others believed such a formulation would be “wrong”?

No — it simply never entered their conceptual space.

The absence of prior work is not because the idea was considered false.

It is because the idea was not even thinkable within their frameworks.

Thus ToE introduces:

a brand-new field,

a brand-new action,

a brand-new coupling,

and a brand-new ontology for entropy.

This is not a continuation of Jacobson, Verlinde, Padmanabhan, or Bianconi.

It is a different category entirely.

8. Does ToE have physical usefulness?

Yes — if and only if:

it produces testable predictions,

it reproduces known physics,

it explains currently unexplained phenomena,

and it yields consistent field equations

— which ToE is already doing for:

light deflection,

mass increase,

time dilation,

entanglement formation time,

black hole energy flows,

entropy-curvature coupling,

cosmological acceleration,

entropy cones,

and more.

There is no known contradiction with experiment so far.

9. Concluding Remarks 

No previous researcher formulated entropy as a fundamental field with a spectral action because entropy was never viewed as a local, dynamical, operator-compatible quantity capable of supporting an action principle.

They did not reject the idea — they never conceived it as possible.

The Theory of Entropicity (ToE) is thus the first framework to:

promote entropy to a universal field,

give it a variational principle (Obidi Action),

endow it with spectral operators,

derive field equations from it,

and unify geometry, gravity, quantum theory, information, and thermodynamics under that field.

This is why no one before ToE has done it.

And it is not because it is wrong — it is because the conceptual leap simply had not been made before.