What question did this study set out to answer?

The aim is to establish a geometrical relationship between information erasure and fundamental constants within physics.

June 20, 2026Open Access

Geometric Cost of Information Erasure: A Schwarzschild-Radius Formulation of the Landauer-Einstein-Schwarzschild Identity

Key Points

The aim is to establish a geometrical relationship between information erasure and fundamental constants within physics.
Derivation of a Schwarzschild-radius formulation for information erasure at temperature T.
Combination of Landauer's principle and Einstein's mass-energy equivalence in the formulation.
Analysis of perturbative effects on the Schwarzschild radius.
The derived formula for Schwarzschild-radius shift is Δr_s = 2G·k_B·T·ln(2)/c⁴.
Establishment of a Planck coincidence: Δr_s(T_P) = 2·ln(2)·l_P, confirming cancellation of fundamental constants.

Abstract

We derive an explicit Schwarzschild-radius form for the geometric effect of erasing one bit of information at temperature T. Combining Landauer's principle, Einstein's mass-energy equivalence, and the perturbative Schwarzschild radius shift, we obtain: Δrₛ = 2G·kB·T·ln (2) /c⁴. The central result is an exact Planck coincidence: Δrₛ (TP) = 2·ln (2) ·lP, where all four fundamental constants cancel algebraically.

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