Gravity from Heat: How Entropy Rewrites the Equations of the Universe

Original: "Extended Gravity Theories from a Thermodynamic Perspective"
· H. R. Fazlollahi
arXiv:2604.09739 · 2026-04-09 · CC BY 4.0 · 2 min
A modified horizon entropy turns into modified gravity and does away with the Big Bang singularity.

The event horizon of a black hole behaves like a thermostat: it has a temperature and an entropy. In 1995, physicist Ted Jacobson showed that if you apply the ordinary rule of heat transfer to this thermostat, Einstein's equations of gravity follow from it on their own. Heat, temperature and a measure of disorder on the boundary of an accessible region of space: that, it turns out, is what attraction is made of.

Horizon entropy is the amount of information that can fit on its surface. It is proportional to area, as if every patch of the horizon stored one bit.

In the new work this idea is taken further. The author replaces the standard entropy formula with a more general one and watches how gravity changes. It turns out that any change in entropy is equivalent to a change in the strength of the gravitational coupling. It is as if the thermostat's scale set the stiffness of a spring.

Ordinary corrections to entropy do not save us from infinite density at the beginning of the Universe. So the author constructs a new entropy in which the horizon is made of tiny quantum oscillators, and a minimum area plays the role of the ground state, like the zero-point energy of a vibrating string. Even an empty horizon cannot be entirely empty.

In the early Universe the expansion rate tends to a finite limit rather than to infinity. Instead of a Big Bang point, there is a phase of rapid but smooth swelling.

At late times the model reproduces the behavior of loop quantum cosmology: at high density, expansion slows down. But unlike that theory, there is no bounce here, only an inflationary phase. A horizon-thermostat with a new entropy scale rewrites the history of the Universe, with no singularity at the beginning.

The minimum horizon area A₀ plays a role analogous to the ground-state energy of a quantum harmonic oscillator: even in an "empty" horizon there remains an irreducible quantum activity. In the model, allowed areas are quantized as A = nA₀, where n ≥ 2, meaning the n=1 state is forbidden due to logarithmic divergence.

The idea that gravity arises from horizon thermodynamics echoes Liu Cixin's novel The Three-Body Problem, where an alien civilization manipulates fundamental laws through curled-up dimensions. Here, horizon entropy acts as code that rewrites gravity.

Scientists
Jacob BekensteinStephen HawkingGerard 't HooftLeonard SusskindBernhard RiemannJoseph Weber
Concepts
fq gravity general relativity barrow entropy alternative gravity theories supergravity wald entropy newtonian limit gravitational theory refined inflationary dynamics eternal inflation gravitational singularity starobinsky inflation quantum time quantum corrections entropic shadow expanding universe spacetime emergence Law of Universal Gravitation spacetime curvature Penrose singularity theorem