Quantum V–Index: A Dimensionless Information–Energy–Entropy Efficiency Metric for Quantum Systems

This is a preliminary study and not the final version. An updated revision will be available shortly. We thank you for your feedback. Quantum V-Index: A Universal Efficiency Metric for Information Processing While classical thermodynamics defines the theoretical minimum cost of information erasure via Landauer’s principle, real-world physical systems ranging from nanomagnetic bits to quantum circuits operate with a consistent overhead to maintain informational integrity. This paper introduces the Quantum V-Index (Vq), a dimensionless metric that unifies von Neumann entropy, energy dissipation, and system stability into a single, platform-independent framework. By normalizing physical variables into bit-equivalents, the V-index reveals a fundamental symmetry in informational processes. At the theoretical limit of optimality, the index converges to a fixed reference point, while high-precision experimental data across diverse platforms suggest the existence of a universal stability constant.This framework bridges the gap between quantum coherence and classical dissipation, providing an objective benchmark for qubit operation efficiency and informational integrity. The Quantum V-Index represents a candidate for a universal law of informational thermodynamics, defining the precise energy entropy cost of stability in any processing system. Note: In quantum thermodynamic treatments the definition of ΔS_Q can follow either a system‑based or an environment‑based entropy convention. The present preprint uses one consistent convention, but readers should be aware that different frameworks assign ΔS_Q differently. A New Horizon in Quantum Gravity (V-index) The underlying mathematical formulas and the formal definition of the V-index : https://doi.org/10.5281/zenodo.18147084