I’ve been working on a strange idea, What if spatial entropy gradients just ∇S, no temperature, no randomness could give rise to a real conservative force in a classical, collision less system?
It’s not a metaphor. The setup is:-
take a weakly inhomogeneous expanding medium with no collisions. Let entropy gradients emerge passively over time. Can those gradients act as sources for a scalar potential and if so, could particles respond to that field in a way that mimics force?
I’ve sketched out a framework for this:  
VGETA, short for V. Gradient Entropy Theory of Asymmetry. It’s classical, deterministic, and potentially falsifiable. The core force the Entropy emergent force arises from the gradient of a scalar entropy based potential ( Entropy gradient Field). There’s no thermal equilibrium, no heat bath, and no stochastic motion involved.
This post is an open invitation to develop, challenge, or dismantle the idea together !!

Why Share It Here??

I know Less Wrong audience values clear reasoning, falsifiability, and conceptual elegance. VGETA is an attempt to work inside that spirit. It’s not a grand theory, it’s a testable structure that might reveal something interesting if it holds up and something instructive if it breaks.
If nothing else, I’d like to think of this as a conversation starter! Is there room for conservative forces to emerge from entropy geometry alone?
I’ve tried out two independent derivations. But the math is just the foundation. What we build on top of it, question, or discard ! that’s where this community’s insight can matter.

Why This Might Matter (If It’s Not Wrong)

The basic claim is entropy gradients (∇S) can act like a source for a scalar potential field, and its gradient yields a conservative force. No thermodynamic bath required. No holography. No fluctuations.
This diverges from models like entropic gravity, which rely on stochastic motion or temperature. If VGETA works, it would suggest a different path to force emergence one tied to large scale structure in phase space, not statistical behaviour at small scales.
The nice thing is this doesn’t require speculative assumptions!! No new particles!! No exotic physics !! Just field theory, thermodynamics, and entropy as a spatial function.

What We Can Test together !

If you’re curious or sceptical, here’s what we could check:
- Can ∇S be defined in systems like Fornax, GD‑1, or Draco?
- Does the resulting Entropy Gradient field produce force profiles that match observation?
- Does the math hold under symbolic scrutiny — conservation laws, time evolution, etc.?
- Where does it fall apart? And how could we fix or reinterpret it?

I’ve published a paper with the derivations and some initial comparisons. But there’s room for refinement, falsification, or extensions and I’d love to see where others might take it.

Resources (If You Want to Dive In , I would suggest the Medium blog first as it might give you some intuition about the frame work)

 -[Summary on Medium]

-[Full Paper – VGETA: And for LaTeX]

I’d especially love help thinking through
- More rigorous entropy modelling in real astrophysical systems
- Better observational tests
- Alternate derivation pathways

Closing Thought

I don’t know if this idea will survive serious testing. But I think it’s worth testing.
If entropy gradients can give rise to structure not just in a statistical sense, but in a geometric, dynamical one that might tell us something new about how force, form, and information interact at scale.
Let’s find out together!! I’m open to criticism^[1], collaboration, or correction. If something’s off, I’ll revise the idea. If something holds, maybe we’ve uncovered a path worth following further.
Thanks in advance for your thoughts.

1. ^{^}

   If you’re interested in reviewing or evaluating the theory more deeply, I’d kindly suggest referring directly to the original paper, as it contains the full derivations and assumptions in context. If you're using AI tools to assist, I’d recommend choosing a model capable of symbolic reasoning simpler LLMs often miss important dependencies or fail on LaTeX-heavy structures. Something like GPT-4 (with tools like SymPy or Python) is more reliable for this kind of task. Also, while philosophical objections are welcome, this is ultimately a mathematical model so critiques are most useful when they engage with the equations. If something in the math seems off, I’d really appreciate a clear demonstration of what’s violated (e.g. energy conservation, dimensional consistency, etc.). Using tools like SymPy, Jupyter, or any symbolic checker can help make issues easier to spot and discuss productively.