IPI Letters

A Thermodynamic Foundation for the Second Law of Infodynamics

Ian Todd — 2026-01-21

Vopson and Lepadatu’s “second law of infodynamics” proposes that the information entropy of physical systems decreases over time, with high-symmetry states representing minimum information entropy. We interpret this information entropy as structure-information: the relative entropy Istruct = DKL(p∥piso) measuring a distribution’s departure from isotropic equilibrium. This paper provides a thermodynamic mechanism for the decrease of structure-information. We derive a bound showing that maintaining a low-dimensional (asymmetric) state requires continuous work input with two components: an informational term and a geometric contraction term governed by the Jacobian of the projection map. Without this work, systems relax toward high-symmetry equilibrium where Istruct → 0. The second law of infodynamics thus emerges from a
thermodynamic asymmetry: symmetric states require no work to maintain, while asymmetric states are thermodynamically costly. This does not contradict the second law of thermodynamics—thermodynamic entropy increases in the bath precisely because structure-information is being dissipated.

Computational Complexity of Determining the Assembly Index

Piotr Masierak — 2026-01-21

The assembly index of assembly theory quantifies the minimal number of composition steps required to construct an object from elementary components. The study proves that the decision version of the assembly index problem is NP-complete, through an explicit correspondence between assembly plans and straight-line grammars. This correspondence implies that the optimization version of the assembly index problem inherits NP- and APX-hardness from the classical smallest grammar problem. The study provides complete, self-contained proofs for both decision and optimization variants of the assembly index problem. These results establish that computing or approximating the assembly index is computationally intractable, placing it within the same complexity class as grammar-based compression.

Grid Physics: The Geometric Unification of Fundamental Interactions via Vacuum Impedance

Pavel Popov — 2026-01-21

Recent proposals in Information Physics posit that the physical universe may be modeled as a discrete computational substrate. We present Grid Physics, a framework exploring the hypothesis that spacetime acts as a Face-Centered Cubic (FCC) information lattice governed by the Principle of Computational Optimization (ΣK → min). Unlike standard models dependent on arbitrary fitting, we demonstrate that fundamental physical constants can be interpreted as emergent geometric impedances of this discrete vacuum. Specifically: a) Proton-to-Electron Mass Ratio (μ ≈ 6π5) and the Fine-Structure Constant (α−1 ≈ 137.036) are modeled as intrinsic geometric properties of the lattice interface; b) We define the ”Entropic Impedance Factor” (γsys ≈ 1.0418)—numerically consistent with the Proton Radius Anomaly—as the information entropy loss inherent in
projecting continuous spherical symmetries onto a discrete grid; c) We show that atomic nuclei can be modeled as crystalline clusters of Alpha-particles, yielding binding energy predictions with > 99.9% correlation to experimental data; d) We propose that Superconductivity in condensed matter (e.g., Twisted Bilayer Graphene) represents a state of Geometric Resonance (N/137) between the material lattice and the vacuum impedance. This framework suggests that physical laws may be viewed as runtime optimization protocols of a discrete system, offering a unified geometric perspective on mass, nuclear stability, and conductivity consistent with the Mass-Energy-Information Equivalence principle.