On Information and Time - Thermodynamics and Information in a Spacelike 5D Informational Metric

This work develops the operational and thermodynamic layer of the OIT-SIM framework: OIT–Thermodynamics and Information in a Spacelike 5D Informational Metric (OIT-TISIM). It reconstructs physically relevant informational variation and relates it to the spacelike informational geometry introduced in OIT-SIM. The framework distinguishes between the ontological informational coordinate , introduced in OIT-SIM as part of the minimal 5D informational metric, and the operational estimators used to approximate its variation in physical systems. Starting from statistical deviation relative to a reference model, Isurpr = (1/ln 2) · D(P || Q)the model introduces structural novelty , persistent correlations , and stochastic or dissipative contributions . These components define an effective informational quantity: Ieff = 𝓕M(Inew, Iflat, INoise) where denotes a physical coarse-graining scheme. The formulation is non-anthropocentric: informational quantities depend on physical resolution, interaction structure, persistence, and accessible degrees of freedom, not on subjective observation. The geometrically relevant component is: dIm = dImetric = ℍ(dIeff) which isolates the coherent, persistent, and transportable part of informational variation that can enter the spacelike 5D metric: dΣ² = c²dt² − dℓ² − keff²dIm² Equivalently, dτ5D² = dτ4D² − dqI,eff² , dqI,eff = (keff/c) dIm The framework is connected to Landauer’s principle, Bekenstein bounds, free-energy considerations, entropy production, and effective informational scales such as keff, kL(T), and kLB(T). These are interpreted as operational or thermodynamic calibrations, not replacements for the bare geometric coefficient k0 of OIT-SIM. Informational kinematics is described by vI and aI along the informational coordinate (Annex 6), while spatial drifts such as asp arise from gradients of k(x,I) in the geodesic equations (Annex 1). When the effective informational metric coefficient becomes inhomogeneous, k = k(x,I), the 5D geodesic equations yield a projected spatial informational drift, asp = x¨ = + k(∇k) Im˙2 , interpreted as an effective geometric drift in informationally structured media rather than as a new fundamental 4D force. OIT-TISIM proposes a spacelike informational-geometric bridge between thermodynamics, information theory, and geometric extensions of spacetime, while preserving the distinction between ontological geometry and operational reconstruction. ORCID: https://orcid.org/0009-0002-3646-1493