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arXiv:2505.06509

The Quantum Toll Framework: A Thermodynamic Model of Collapse and Coherence

L. S. Montejo

Published May 10, 2025• 0 citations
arXivHTMLPDF

Abstract

We present a thermodynamic rendering model in which the traditional quantum observer is reframed as a special case of a coherence-constrained interface. Collapse is treated not as an interpretive postulate but as a structural threshold - reached when the energetic cost of sustaining coherence exceeds a system's available budget. The Quantum Toll Framework (QTF) formalizes this by recasting observation as a bounded rendering process, governed by entropy, energy, and discrete action. Extending Landauer's principle, we show that the thermodynamic cost of observation includes not only information erasure but also the stabilization of rendered states. Collapse is thus redefined as a solvable, testable transition. This model accounts for classical emergence, time asymmetry, and measurement without invoking consciousness or symbolic cognition. Empirical consequences are discussed, including confirmation of a quantized collapse floor in historical cloud chamber data.

DOI
10.48550/arxiv.2505.06509

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We present a thermodynamic rendering model in which the traditional quantum observer is reframed as a special case of a coherence-constrained interface. Collapse is treated not as an interpretive postulate but as a structural threshold - reached when the energetic cost of sustaining coherence exceeds a system's available budget. The Quantum Toll Framework (QTF) formalizes this by recasting observation as a bounded rendering process, governed by entropy, energy, and discrete action. Extending Landauer's principle, we show that the thermodynamic cost of observation includes not only information erasure but also the stabilization of rendered states. Collapse is thus redefined as a solvable, testable transition. This model accounts for classical emergence, time asymmetry, and measurement without invoking consciousness or symbolic cognition. Empirical consequences are discussed, including confirmation of a quantized collapse floor in historical cloud chamber data.
We present a thermodynamic rendering model in which the traditional quantum observer is reframed as a special case of a coherence-constrained interface. Collapse is treated not as an interpretive postulate but as a structural threshold - reached when the energetic cost of sustaining coherence exceeds a system's available budget. The Quantum Toll Framework (QTF) formalizes this by recasting observation as a bounded rendering process, governed by entropy, energy, and discrete action. Extending Landauer's principle, we show that the thermodynamic cost of observation includes not only information erasure but also the stabilization of rendered states. Collapse is thus redefined as a solvable, testable transition. This model accounts for classical emergence, time asymmetry, and measurement without invoking consciousness or symbolic cognition. Empirical consequences are discussed, including confirmation of a quantized collapse floor in historical cloud chamber data.
This preprint develops a thermodynamically grounded bridge between unitary quantum dynamics and irreversible classical record formation. Any detector or observer is modeled as a finite-solvency Quantum Information Interface (QII) with a maximum sustainable registration rate set by Landauer’s bound and its available power density. The framework introduces an operational external structured load, a dimensionless collapse-load ratio, and a solvency-defined transition layer termed the Goldilocks Rendering Zone. Classical structure emerges only when local registration demand remains below the interface’s thermodynamic ceiling, while higher loads remain in the reversible amplitude domain. The model yields testable predictions for the quantum–classical boundary, including a temperature-dependent narrowing of cloud-chamber track morphology not implied by decoherence alone.
The mechanism underlying wave function collapse remains one of the most persistent open questions in the foundations of quantum mechanics. Standard interpretations often treat the collapse as either an inexplicable axiom (Copenhagen) or an illusion (Many-Worlds). This paper proposes a third alternative based on the Principle of Informational Parsimony in a finite-capacity universe. We posit that the wave function represents a system in an informationally compressed state, maintained to optimize the computational resources of spacetime. Within this framework, “collapse” is reinterpreted as a Data Rendering Event: a thermodynamic transition where the system decompresses the state vector into a localized coordinate in response to an interaction request (observation). Using Landauer’s Principle, we derive the minimum thermodynamic cost of this rendering process. We further argue that the Heisenberg Uncertainty Principle arises naturally as a resolution limit inherent to the transition between compressed (momentum-space) and rendered (position-space) data formats. Finally, we propose that the discrete granularity of this rendering process implies a detectable quantization noise at the Planck scale.
This preprint examines the thermodynamic limits of information registration and their implications for quantum mechanics, black hole physics, and cosmology. Building on Landauer’s principle, it argues that registration and erasure are physically inseparable operations, each incurring the same energetic toll of kBTln⁡2 per bit. From this perspective, quantum “collapse” is reframed as collapse insolvency, the condition that stable records cannot be formed beyond an energy constrained ceiling. The paper develops a Six Tier Insolvency Model, distinguishing between global constraints (Bekenstein–Hawking entropy, Landauer throughput, empirical ceilings) and local bottlenecks (Hawking flux, flux dilution, observer collapse limit). It derives striking insolvency ratios (~10⁻⁵⁶ globally and ~10⁻⁴⁷ locally), quantifying the gap between the entropy accessible in principle and that which any finite observer can render. The analysis introduces the Goldilocks Rendering Zone (GRZ), a universal band where collapse can occur: too little flux leaves no record, too much flux exceeds solvency. This provides a unified account that links quantum measurement, biological information processing, and black hole horizons under the same energetic constraint. The framework is falsifiable. It predicts a hard ceiling of ~10¹² bits·s⁻¹·m⁻² for sustained registration under standard conditions (300 K, 1 W/m²). A single reproducible counterexample would suffice to overturn the model.
Description This paper proposes a framework in which quantum measurement collapse emerges as an intrinsic dynamical process in a quantum informational field. Using entropy-regularized optimal transport (Schrödinger bridge theory) together with threshold phenomena in high-dimensional systems, collapse is interpreted as an entropy-minimizing transport process that concentrates informational coherence. Within this framework, quantum waves are treated as carriers of quantum information forming a chaotic informational field from which coherent structures may emerge. The approach connects Schrödinger bridge dynamics, threshold behavior in subsystem purity, and the path-integral formulation of quantum mechanics. Collapse is therefore interpreted as a field-intrinsic process rather than a consequence of observer intervention. The paper further explores implications for quantum information theory, Quantum Darwinism, and informational approaches to consciousness, suggesting experimentally testable signatures for coherence thresholds in complex quantum systems.
Abstract This paper presents a novel interpretation of wavefunction collapse grounded in quantum information theory. We propose that collapse is not triggered by observation itself, but by a quantized increase in a system's informational entropy. Specifically, we introduce a threshold condition: collapse occurs only when the von Neumann entropy of the system exceeds a critical value, δIc, due to entanglement with the environment. This reframing allows wavefunction collapse to be understood as an objective, testable process driven by entropy flow, rather than subjective measurement. We formalize this framework using mathematical postulates and simulate its behavior in canonical quantum setups, including the double-slit experiment, spin measurement, and Schrödinger’s cat. The model not only aligns with known phenomena but also makes falsifiable predictions—suggesting that collapse is conditional and occurs only beyond an entropy threshold. This provides a new lens on the quantum measurement problem and opens experimental paths for validating information-induced collapse.