Ginestra Bianconi, a network scientist turned theoretical physicist, has developed “Gravity from Entropy” — a new theory that derives gravity from an action principle quantifying the information content of the universe’s microscopic degrees of freedom, treating geometry and matter on equal footing through a geometric quantum relative entropy between two metrics, which reduces to Einstein’s equations at low energies but predicts a dynamical, always-positive dark energy term and possible singularity avoidance.
Background and motivation
Bianconi spent her career in discrete network science and simplicial complexes, studying how topology shapes dynamics in complex systems
She resisted moving to continuum physics, believing nature might be fundamentally discrete, but a colleague at ICTP Trieste challenged her to formulate her structure-dynamics-interplay theory in the continuum
She realized the continuum version naturally connects to gravity, since the interplay between geometry (structure) and matter fields (dynamics) is the central problem of general relativity
The transition to continuum physics happened when she decided to confront quantum gravity directly, finding it a “fantastic playground” despite being new to the field
Core idea: gravity from entropy
The theory starts from an action that quantifies the information content of the microscopic degrees of freedom of geometry and matter
It uses a geometric quantum relative entropy as the Lagrangian, comparing two metrics: the true spacetime metric and a metric induced by matter fields and curvature
This creates a symmetric description where matter tells geometry how it would like the metric to be, and geometry tells matter how to move — implementing Wheeler’s “matter tells spacetime how to curve, spacetime tells matter how to move” at the action level, not just the equations of motion
The action is fundamentally statistical mechanical: it captures the microscopic degrees of freedom and their information content, not just thermodynamic coarse-graining
The two metrics and their geometric origin
True metric: the actual spacetime metric defining Ricci scalar, Riemann curvature, and causal structure — no background Minkowski assumption
Induced metric: a geometrization of matter fields and curvature, extending Gauss’s first fundamental form (which gives the metric induced by a scalar field on a manifold) to higher-order matter descriptions (scalar, one-form, two-form at each point)
The induced metric draws on von Neumann algebra literature and Witten’s work on Araki entropy for relative entropy in quantum field theory
Both metrics are treated symmetrically as quantum operators; the relative entropy measures how much information in one is codified in the other
The relative entropy locally decreases in time (metrics try to align), but the integrated action increases — consistent with Boltzmann entropy increase cosmologically
Mathematical simplification: trace of logarithm = logarithm of determinant, connecting relative entropy to a Boltzmann-like counting of microstates
The action yields modified gravity equations that reduce to Einstein’s equations in the low-energy limit but differ at high energies
A new emergent field, the G field, appears as a Lagrange multiplier; when expressed in terms of G, the action resembles Einstein-Hilbert but with:
A dressed metric (true metric contracted with G field) mediating matter-geometry coupling
A dynamical cosmological constant (dark energy) depending on G, always positive and vanishing at low energies
Key predictions and implications
Dark energy: emerges naturally as a dynamical, positive cosmological constant driven by the G field — potentially relevant to Hubble tension
Modified gravity: testable deviations from GR at high energies/early universe; a Chinese group has already shown inflationary behavior without an inflaton field
Black hole entropy: reproduces the area law from volume integration because the Lagrangian depends on the full Riemann tensor (including Weyl curvature), making degrees of freedom inhomogeneous inside the horizon — no holographic screen assumption needed
Planck-scale corrections: appear even in flat geometry because geometry and matter are treated together
Singularity avoidance: the G field becomes dynamical near singularities; the Schwarzschild solution is only approximate, and static black hole solutions may not exist — singularities potentially resolved
Comparison with other approaches
vs. Verlinde’s entropic gravity: Verlinde uses horizon entropy and holographic screens (thermodynamic); Bianconi uses a microscopic statistical mechanics action with no screen, focusing on matter-geometry interplay
vs. other modified gravity: motivated by information theory and statistical mechanics, not arbitrary higher-curvature terms
vs. discrete quantum gravity (causal sets, CDT, Wolfram): gravity from entropy recovers Einstein’s equations in the low-energy limit, which many discrete approaches struggle to do
Thermodynamics vs. statistical mechanics: thermodynamics (Clausius, heat engines) gives macroscopic laws without microscopic explanation; statistical mechanics (Boltzmann) derives them from microscopic degrees of freedom — Bianconi’s approach is fundamentally statistical mechanical, treating information theory as the common language
Open problems and current work
Second quantization: the central challenge — how to promote the classical metric operator to a fully quantum field theory; this “keeps her awake at night”
Cosmological implications: detailed predictions for Hubble tension, early universe, structure formation
Entanglement connection: relation to hierarchy entropy and entanglement entropy in QFT; the Araki entropy link suggests deep connections
Standard Model coupling: formulating how to embed all matter fields (not just bosonic scalars/fluids) into the induced metric
Discrete limit: whether and how to return to a discrete formulation from the continuum theory
Advice and philosophy
To PhD students: read deeply, follow what you love, express your own vision of reality, and enjoy the process — science should be fun
Best advice received: “Why don’t you go in the continuum?” (from a stranger at a seminar) and “explore other communities” — attending a gravity session at a DPG meeting while presenting on networks sparked the key insight
Approach problems abstractly, look at nature with surprise, and cross disciplinary boundaries to find unexpected connections
