Physics of information at eleven parameters
Abstract
The bounds of the physics of information, Bekenstein's on the entropy of a bounded system, Bekenstein and Hawking's on the entropy of a horizon, the Margolus-Levitin and Bremermann limits on the rate of computation, Lloyd's ultimate laptop and Landauer's cost of erasure, all mix the constants ℏ, c, k B and G that the relativity at eleven parameters carries in its relativity principle. This paper shows that three structures of the eleven give these bounds a common origin. The first is the thermal circle of the thermal theory of the eleven, the Euclidean time circle of radius ℏc/(2πk B T ), which has two ends: it cannot be shorter than the Planck length, which is the maximal temperature T P /(2π), and it cannot exceed the region that confines the system, which is Bekenstein's bound S ≤ 2πk B RE/(ℏc) in form; at a horizon, R = r g , the second end is Bekenstein-Hawking's A/(4L 2 P ) exactly, and at the Planck length the two ends meet in the relic of one bit. The second is the acceleration bound a ≤ mc 3 /ℏ, which bounds the rate at which a body's momentum, its register, can be rewritten by one Compton momentum per Compton time, and which is the Margolus-Levitin limit of the momentum sector to the factor 2/π; summed over the bodies of a computer of mass M it gives M c 2 /ℏ operations per second, π/2 times Lloyd's 2M c 2 /(πℏ). The third is the compact spin sector, whose 2s + 1 states are the eleven's bits, and, in the quantum step of the ninth article, the two scales L P and R of Yang's algebra, whose ratio squared gives the holographic count of the universe, π(R/L P ) 2 /(ln 2) = 3×10 122 bits for the Hubble radius, and the inverse of the cosmological constant in Planck units. Lloyd's ultimate laptop, one kilogram in one litre, is then read in the eleven: its temperature 5.9 × 10 8 K is 0.62 of the maximal temperature of the electron bath, its thermal circle of 6 × 10 -13 m sits between the Planck length and the litre, and its memory of 2 × 10 31 bits is eleven orders below Bekenstein's bound because it is not a black hole. Landauer's cost has a maximum in the eleven, (mc 2 /(2π)) ln 2 per bit for a memory of bodies of mass m, 56 keV for electrons, and 1.35 × 10 18 GeV at the ceiling. The paper ends with the bits of the horizon and of the bounce: the relic of the thermal theory holds 1.13 bits, and the bounce ball of a stellar black hole carries 10 39 nats of thermal entropy through a sphere whose area allows 10 25 , which is the known failure of the entropy bounds where the null energy condition fails, and the place where the eleven's information passes into the daughter universe unbounded.
Related
- Analogue models of gravity at eleven parameters
- The concepts at eleven parameters: the primary, the secondary and the optional, their hierarchy and their graph
- The eleven parameters of a body: the gauged Weyl algebra, its exact identities and the Palatini form of Higgs inflation
- Feynman diagrams of the unified theory at eleven parameters
- Quantum reference frames at eleven parameters: the Wigner rotation measures the frame
BibTeX
@misc{reynaud2026physics,
title = {{Physics of information at eleven parameters}},
author = {Patrick .B Reynaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05749768v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics of information at eleven parameters
AU - Patrick .B Reynaud
PY - 2026
DA - 2026/09/14
PB - HAL
UR - https://hal.science/hal-05749768v2
AB - The bounds of the physics of information, Bekenstein's on the entropy of a bounded system, Bekenstein and Hawking's on the entropy of a horizon, the Margolus-Levitin and Bremermann limits on the rate of computation, Lloyd's ultimate laptop and Landauer's cost of erasure, all mix the constants ℏ, c, k B and G that the relativity at eleven parameters carries in its relativity principle. This paper shows that three structures of the eleven give these bounds a common origin. The first is the thermal circle of the thermal theory of the eleven, the Euclidean time circle of radius ℏc/(2πk B T ), which has two ends: it cannot be shorter than the Planck length, which is the maximal temperature T P /(2π), and it cannot exceed the region that confines the system, which is Bekenstein's bound S ≤ 2πk B RE/(ℏc) in form; at a horizon, R = r g , the second end is Bekenstein-Hawking's A/(4L 2 P ) exactly, and at the Planck length the two ends meet in the relic of one bit. The second is the acceleration bound a ≤ mc 3 /ℏ, which bounds the rate at which a body's momentum, its register, can be rewritten by one Compton momentum per Compton time, and which is the Margolus-Levitin limit of the momentum sector to the factor 2/π; summed over the bodies of a computer of mass M it gives M c 2 /ℏ operations per second, π/2 times Lloyd's 2M c 2 /(πℏ). The third is the compact spin sector, whose 2s + 1 states are the eleven's bits, and, in the quantum step of the ninth article, the two scales L P and R of Yang's algebra, whose ratio squared gives the holographic count of the universe, π(R/L P ) 2 /(ln 2) = 3×10 122 bits for the Hubble radius, and the inverse of the cosmological constant in Planck units. Lloyd's ultimate laptop, one kilogram in one litre, is then read in the eleven: its temperature 5.9 × 10 8 K is 0.62 of the maximal temperature of the electron bath, its thermal circle of 6 × 10 -13 m sits between the Planck length and the litre, and its memory of 2 × 10 31 bits is eleven orders below Bekenstein's bound because it is not a black hole. Landauer's cost has a maximum in the eleven, (mc 2 /(2π)) ln 2 per bit for a memory of bodies of mass m, 56 keV for electrons, and 1.35 × 10 18 GeV at the ceiling. The paper ends with the bits of the horizon and of the bounce: the relic of the thermal theory holds 1.13 bits, and the bounce ball of a stellar black hole carries 10 39 nats of thermal entropy through a sphere whose area allows 10 25 , which is the known failure of the entropy bounds where the null energy condition fails, and the place where the eleven's information passes into the daughter universe unbounded.
ER -