The Arrow of Time as a Structural Consequence of the Embedding: Landauer's Principle within the Absolute Frame Theory

Version of July 9th, 2026, following technical developments withint the Absolute Frame Theory programme. We derive the irreversibility of time and Landauer's principle as structural consequences of the embedding of the four-dimensional observable manifold ℳ into the higher-dimensional substratum 𝒜 within the Absolute Frame Theory (AFT). The projection from 𝒜 to ℳ is many-to-one for N > 4, and the information stored in the fiber directions of the embedding is inaccessible from observations within ℳ. We distinguish carefully between energy and information: the third axiom of AFT conserves energy-momentum (no net flux to 𝒜), while a fourth axiom — informational irreversibility — asserts that the fine-grained correlation transferred to the inaccessible fiber, quantified by the entanglement entropy S_ℳ of the observable subsystem, cannot be recovered by any operation within ℳ. The second law, dS_ℳ/dt ≥ 0, is the embedding-theoretic form of Axiom IV, with energy conserved throughout; this is the arrow of time in a structural, non-coarse-grained sense, objective but relative to the ℳ–𝒜 boundary. We obtain an effective channel temperature from the Euclidean (Wick) period of the embedding dynamics, k_B T_eff = ħω_ch / 2π. At cosmological scales this recovers the Gibbons–Hawking temperature of the de Sitter horizon, the factor 2π arising from the Euclidean period rather than by hand; for an accelerated observer it recovers the Unruh temperature; during inflation it is the de Sitter (Gibbons–Hawking) temperature of the Starobinsky plateau, set by the inflationary Hubble rate H_inf ≃ 1.5×10¹³ [GeV] of the emergent R² regime. Landauer's principle, in its AFT form, bounds the erasure energy — dissipated as heat within ℳ, the information crossing to the fiber — by k_B T_eff ln 2. The framework provides a structural account of the low-entropy initial condition as a separate past hypothesis tied to the onset of the embedding, and identifies the cosmological and thermodynamic arrows of time.