Information Theory — Why Is Information Physical?

Erase one bit of information at room temperature and you must release at least 2.85 × 10⁻²¹ joules of heat into the environment. Not as an engineering limit. As a thermodynamic floor. Rolf Landauer proved this in 1961, ENS Lyon measured it in 2012, and a 2025 collaboration extended it to entangled quantum many-body systems. The claim that information is physical stopped being a slogan some time around the second decimal place.

Shannon's accident: entropy is entropy

Shannon (1948) defined the information in a message as H = −Σ pᵢ log₂ pᵢ — the same functional form Boltzmann had used for thermodynamic entropy in 1877, up to a constant (k_B · ln 2). Shannon picked the name "entropy" on John von Neumann's advice: "no one knows what entropy really is, so in a debate you will always have the advantage."

The form-match is not aesthetic coincidence. Boltzmann counts microstates compatible with a macrostate. Shannon counts messages compatible with a distribution. They are the same count in different units. A bit and a joule per kelvin differ by k_B · ln 2 — a unit conversion, not a metaphysics.

Landauer's bill

Landauer's 1961 result: any logically irreversible operation must dissipate at least k_B T ln 2 of heat. Erasure is the canonical case, because you collapse two possible inputs (0 or 1) into one output (0). The lost bit becomes a bit of entropy in the bath.

Three consequences worth holding:

Maxwell's demon is no longer free. Charles Bennett (1982) closed the 1867 paradox: the demon must eventually erase its memory of past measurements, and that erasure pays back exactly the entropy it appeared to save. Information was the missing line on the ledger.
Modern chips waste roughly 1,000× the Landauer floor. A current transistor switch dissipates ~10⁻¹⁸ J. The thermodynamic minimum at 300 K is 2.85 × 10⁻²¹ J. Three orders of magnitude of headroom before physics, not engineering, sets the energy ceiling.
2012, Bérut et al., ENS Lyon, Nature. A single colloidal particle trapped in a double-well optical potential, erased, with the dissipated heat measured directly. Match to k_B T ln 2 within experimental error, 51 years after the prediction.

The 2025 quantum extension (TU Vienna / FU Berlin / UBC, Nature Physics) used a Bose-gas quantum field simulator and a global mass quench to confirm the principle when the bit being erased is entangled with its bath. Classical Landauer is a limit; the full law depends on system-bath entanglement structure.

It from bit

John Wheeler — who coined "black hole" and co-wrote Gravitation — proposed in 1989 that "every it derives its function, its meaning, its very existence" from yes/no answers. Not that physics can be re-described in information terms. That information is the substrate and matter is the encoding.

What pushes the conjecture from slogan toward physics:

Bekenstein-Hawking entropy. A black hole's entropy is proportional to its horizon area, not volume — S = A/4 in Planck units. The information content of a region is bounded by its boundary. The universe stores three-dimensional content on two-dimensional surfaces. See concept holographic principle.
AdS/CFT as a quantum error-correcting code. Almheiri, Dong, and Harlow (2015) showed the duality between gravity-in-a-volume and field-theory-on-the-boundary is, mathematically, a QEC code. Spacetime geometry is redundantly encoded entanglement. See concept spacetime from entanglement.
Quantum measurement is a binary question. Every projective measurement extracts a bit. The wavefunction is the prior; the measurement is the bit. Quantum mechanics is information theory with i in the exponent.

What's contested

The phrase "information is physical" is established. Wheeler's stronger claim — that information is physics — is not. Three live fronts:

Vopson's "second law of infodynamics" (Portsmouth, 2022) claims information entropy decreases over time, opposite to thermodynamic entropy, and that information has mass (~10⁻³⁵ kg/bit at 300 K). The SARS-CoV-2 genomic evidence has been criticised as selection-effect laden, and the predicted electron-positron annihilation asymmetry has no independent replication as of 2026. Most physicists place this between speculative and fringe.
Discrete vs continuous substrate. Zuse (1969), Fredkin, and Wolfram argue the universe is literally a cellular automaton at Planck scale. Bell-inequality violations and the strong empirical bounds on local hidden variables make naive digital physics hard to sustain. The weaker version — that some discrete information-theoretic structure underlies spacetime — survives.
Black hole information paradox. Hawking argued in 1975 that evaporation radiation is thermal and the infalling information is destroyed. The Page-curve calculations of 2019–2020 (Penington; Almheiri et al.) suggest the information escapes via subtle correlations, but the mechanism is still unsettled. See concept black hole information paradox.

Why this has to do with other realms

Computation is bookkeeping for what can and cannot be erased cheaply. Every cache flush, every neuron's reset to baseline, every line of garbage-collected memory is a Landauer payment. The human brain runs at ~20 W and erases something like 10¹⁶ bits per second — extravagant compared to the thermodynamic floor, frugal compared to silicon. A frontier model training run today dissipates roughly nine orders of magnitude more energy than physics demands. Reversible computing (Bennett, 1973) and adiabatic quantum computation are the only known routes toward the floor. The economics of AI scaling and the metabolic economics of thinking are the same equation in different units — see concept brain energy budget.

An open question

If spacetime is built from entanglement and entanglement is a particular structure of information, what fails first if we treat information as more fundamental than spacetime itself? Wheeler bet his last twenty years that something foundational would crack. Where would the first crack appear — in a tabletop experiment, in a black hole observation, or inside an AI system complex enough to notice its own computational substrate?

Key sources

Shannon, A Mathematical Theory of Communication (1948, Bell System Technical Journal) — the founding paper.
Landauer, "Irreversibility and heat generation in the computing process" (1961, IBM J. Res. Dev.) — the original thermodynamic limit.
Bennett, "The thermodynamics of computation — a review" (1982, Int. J. Theor. Phys.) — Maxwell's demon resolved.
Bérut et al., "Experimental verification of Landauer's principle linking information and thermodynamics" (Nature, 2012).
Wheeler, "Information, physics, quantum: the search for links" (1989, Proc. 3rd Int. Symp. Foundations of Quantum Mechanics, Tokyo) — the "it from bit" essay.
to verify: 2025 Nature Physics paper on quantum many-body Landauer (TU Vienna / FU Berlin / UBC collaboration, exact author list).

Abhishek