Einstein's Equations from Information Capacity
Capacity-metric duality and the Clausius derivation
Shows that Einstein's field equations emerge from the Clausius inequality when heat flow is measured by information-theoretic timing capacity.
Feb 27, 2026 · Preprint
Plain English
This paper shows that gravity — the force that holds you to the Earth and bends light around black holes — is a consequence of how information flows through space.
The problem
Einstein's equations describe how matter and energy curve spacetime. They work incredibly well, but we don't know why. Why these equations and not some other ones? Physicists have long suspected that gravity might emerge from something deeper — like thermodynamics or information theory.
The key idea
Imagine a tiny patch of space near a black hole horizon. There is a maximum rate at which quantum information can flow across that patch — called the "timing capacity." This paper proves that this information speed limit is exactly proportional to the temperature of the horizon, with no adjustable parameters.
What the paper does
Starting only from quantum information theory, it derives Einstein's field equations step by step. The punchline: Einstein's theory of gravity is the unique theory where the thermodynamics of horizons closes perfectly. Try to modify gravity — add extra terms, change the coupling — and the information bookkeeping breaks down. General Relativity is the only consistent answer.
Why it matters
This gives a concrete, calculable link between quantum information and gravity. It suggests that spacetime itself may be built from quantum entanglement, and that Einstein's equations are not just a good guess — they are the only possible outcome once you take information seriously.
What could go wrong
The derivation works in the near-horizon (Rindler) limit and assumes thermal equilibrium. Extending it to fully dynamical, far-from-equilibrium situations remains open. The paper has not yet been peer-reviewed.