A Dimensionless Information Energy Entropy Index (V-index): Corrected Definition, Landauer Anchored Lower Bound, and a Variational Protocol Framing (V-index Part 1)

This release (V2) presents a physically consistent, additive bit scale that unifies three pillars of information thermodynamics into a single, dimensionless quantity: surprisal (Ibits), bit‑equivalent heat (abits = Q / (kB * T * ln 2) ), and environmental entropy change (Sbits = DeltaSₑnv / (kB * ln 2) ). In the standard single bath, isothermal erasure class, the exact identity DeltaSₑnv = Q / T implies Sbits = abits, which collapses the feasible geometry to the diagonal and yields a sharp, domain‑universal inequality: V = Ibits + abits + Sbits, V >= Ibits + 2*b, equality only for quasi‑static (Landauer‑optimal) protocols. A protocol level variational principle shows that the bit equivalent action AP = abits + Sbits is minimized precisely by these quasi static transformations, providing a principled explanation for the invariant informational floor. The framework is empirically anchored by named, high precision experiments, colloidal one bit memories (Bérut et al. , Nature, 2012), which converge to the universal minimum V = 2 (for Ibits = 0, b = 1) ; and nanomagnetic single‑bit reset (Hong et al. , Science Advances, 2016), which at 300 K typically yield abits ≈ 1. 44 and under the single‑bath, isothermal constraint Sbits = abits V ≈ 2. 88. A streamlined Monte Carlo verification enforces physical admissibility (single bath, isothermal) and reproduces the strict floor, with saturation only at the Landauer point. By consolidating information loss, dissipated heat, and entropy production into one operational coordinate, the V‑index functions as a law like invariant within its domain and as a rigorous benchmarking tool for classical, mesoscopic, and emerging quantum platforms. It offers a clear metric for comparing devices, an interpretable geometry tied to first principles, and a compact formulation that suggests the structure of a general efficiency principle at the interface of information theory and thermodynamics. --------------------------------------------------------------------------------------------------------------------- A Dimensionless Information Energy Entropy Index (V-index): Corrected Definition, Landauer Anchored Lower Bound, and a Variational Protocol Framing (V-index Part 1) https: //doi. org/10. 5281/zenodo. 18284260 A Universal Balance in Holographic Quantum Gravity The V-index and its Invariance Across Holographic Frameworks (V-index Part 2) https: //doi. org/10. 5281/zenodo. 18288805 Functional Vulnerability Index (V-index) for Genetic Code Degeneracy and Protein Functional Integrity: Applications to TP53 and HIV-1 Protease (V-index Part 3) https: //doi. org/10. 5281/zenodo. 18156730