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
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
One of the outstanding challenges to information processing is the eloquent suppression of energy consumption in the execution of logic operations. The Landauer principle sets an energy constraint in deletion of a classical bit of information. Although some attempts have been made to experimentally approach the fundamental limit restricted by this principle, exploring the Landauer principle in a purely quantum mechanical fashion is still an open question. Employing a trapped ultracold ion, we experimentally demonstrate a quantum version of the Landauer principle, i.e., an equality associated with the energy cost of information erasure in conjunction with the entropy change of the associated quantized environment. Our experimental investigation substantiates an intimate link between information thermodynamics and quantum candidate systems for information processing.
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
The Thermodynamic Cost of Knowing: Observation as Irreversible Payment This preprint is a formal technical note establishing a rigorous, machine-verified bridge between Quantum Information Theory (Englert-Greenberger duality) and Classical Thermodynamics (Landauer's Principle). Abstract The UMST/DUMSTO Thermodynamic Gate has been extended to enforce physical quantum boundary conditions. Every mathematical proposition presented in this note is mechanically verified in Lean 4 with Mathlib. Across 53 core modules (58 .lean files), the underlying formalization contains 515 theorems, 33 lemmas, 6 explicit axioms, and 0 sorry gaps. We formally prove that every fraction of a bit of which-path information causes a proportional destruction of interference, and this destruction carries an exact Landauer thermodynamic cost. The Core Result: The Principle of Maximal Information Collapse The central theorem of this framework demonstrates that information extraction cannot be decoupled from thermodynamic dissipation. Specifically, the acquisition of which-path information strictly binds the residual coherence capacity of the quantum state, forcing a minimum Landauer erasure cost when the environment is reset. When an observer extracts which-path information from a quantum system, the residual coherence capacity is strictly bounded by: Residual Coherence = 1 − [ MI_extracted / (k_B T ln 2) ] ∈ [0, 1] This formally verifies that observation is an irreversible thermodynamic payment, anchoring the abstract axioms of quantum measurement (collapse) to the physical constraints of heat generation. Formally Proved Englert Complementarity: V² + I² ≤ 1 Which-Path Collapse: V → 0 after projection (Lüders channel) Cost-Coherence Identity: Q = k_B T ln(2) · (1 − Residual Capacity) Landauer Bound: Erasure cost matches thermodynamic heat dissipation Quantum Mutual Information: I(A:B) = S(A) + S(B) − S(AB) ≥ 0 General Residual Coherence: measurement-update coherence bound for arbitrary bases Erasure Channel: complete depolarization entropy bound Verification Stack & Source Availability While this document details the theoretical and mathematical framework, the complete proof source code is publicly available via the associated tytolabs GitHub Repository. Formal Proof: Lean 4 + Mathlib (53 modules, 515 theorems, 33 lemmas, 6 explicit axioms, 0 sorry). Property Testing: Haskell/QuickCheck (14 physical admissibility properties). Numerical Simulation: Python (stdlib + QuTiP) — 87 unit tests, 4 simulations. Cross-Language Specs: Coq/Rocq (9 modules, 0 Admitted) and Agda (11 modules) parity translations.
A fundamental gap in quantum thermodynamics is resolved through the derivation of a single operational constraint that closes information gain, memory cost, and measurement back-action into a unified informational budget. It is demonstrated that bandwidth-limited acquisition and measurement-driven control emerge as fundamental consequences of this budget. A universal Critical Bandwidth is identified, marking the threshold where classical dissipation necessitates a transition to quantum-entangled states. This framework is validated by an empirical audit of the human cortex, identifying a 35:1 communication-to-computation energy ratio as the definitive thermodynamic signature of the Entanglement Heat Premium. The discovery of a scale-invariant efficiency constant, establishes the human brain as a near-optimal quantum-limited engine. These results provide a unified scaling law for the energetic limits of intelligence, bridging the gap between superconducting qubits and biological consciousness.
Quantum error correction (QEC) is widely regarded as the indispensable cornerstone for achieving scalable, fault-tolerant quantum computation. However, conventional fault-tolerance theorems traditionally rely on abstract circuit models that frequently abstract away fundamental physical laws, treating noise channels and error syndromes as purely mathematical parameters. In this paper, we establish the Physical Limit of Quantum Error Correction (PLQEC) framework, investigating whether there exists an absolute, nature-imposed lower bound on the residual error probability, denoted as p_min, below which reliable quantum information preservation becomes physically unattainable due to deeply rooted thermodynamic, informational, and spacetime constraints. By systematically integrating Landauer's principle, von Neumann entropy bounds, the intrinsic thermodynamics of quantum measurement, and holographic gravity principles, we derive universal fundamental limits on quantum error correction thresholds. We demonstrate that physical constraints such as minimal energy dissipation per syndrome extraction cycle, quantum speed limits, decoherence velocities, and spacetime curvature cutoffs impose strict, unyielding boundaries on fault-tolerant quantum architectures. This work bridges the profound gap between abstract quantum information theory and fundamental physical law, opening a new frontier in understanding the ultimate operational boundaries of quantum information processing in our physical universe.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature . We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.