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Energy Dissipation Threshold Model for Wave Function Collapse in Open Quantum Systems

Luis Ratia

Published Aug 10, 2026• 0 citations
Publisher

Abstract

The transition from a quantum superposition to a definite classical state remains one of the foundational challenges in physics. We propose a dynamical, objective reduction model where wave function collapse is driven by the exchange and dissipation of energy (∆Edis) between a quantum system and an environment/apparatus. Replacing the abstract notion of "measurement" with a physical dissipation threshold (∆Edis · τcollapse ≥ ℏ/2), we demonstrate that phase coherence decay is directly coupled to environmental energy flux. The model is integrated with the Lindblad Master Equation and Stochastic Schrödinger Equations, incorporating Planck’s quantum of action (E = hν) as a discrete condition for state reduction. Numerical evaluations for an isolated electron, a fullerene (C60) molecule, and photoelectric emission confirm that the model naturally predicts macro-localization while preserving micro-scale quantum superposition, offering a thermodynamically consistent boundary for the quantum-classical transition.

DOI
10.5281/zenodo.21872441

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The transition from a quantum superposition to a definite classical state remains one of the foundational challenges in physics. We propose a dynamical, objective reduction model where wave function collapse is driven by the exchange and dissipation of energy (∆Edis) between a quantum system and an environment/apparatus. Replacing the abstract notion of "measurement" with a physical dissipation threshold (∆Edis · τcollapse ≥ ℏ/2), we demonstrate that phase coherence decay is directly coupled to environmental energy flux. The model is integrated with the Lindblad Master Equation and Stochastic Schrödinger Equations, incorporating Planck’s quantum of action (E = hν) as a discrete condition for state reduction. Numerical evaluations for an isolated electron, a fullerene (C60) molecule, and photoelectric emission confirm that the model naturally predicts macro-localization while preserving micro-scale quantum superposition, offering a thermodynamically consistent boundary for the quantum-classical transition.
Abstract: The transition from a quantum superposition to a definite classical state remains one of the foundational challenges in physics. We propose a dynamical, objective reduction model where wave function collapse is driven by the exchange and dissipation of energy (Δ�dis) between a quantum system and an observer/environment. Replacing the abstract notion of "measurement" with a physical dissipation threshold (Δ�dis⋅�collapse≥ℏ/2), we demonstrate that phase coherence decay is directly coupled to energy flux. The model is integrated with the Lindblad Master Equation and Stochastic Schrödinger Equations, incorporating Planck's quantum of action (�=ℎ�) as a discrete condition for state reduction. Numerical evaluations for an isolated electron and a C60 fullerene molecule confirm that the model naturally predicts macro-localization while preserving micro-scale quantum superposition, offering a thermodynamically consistent boundary for the quantum-classical transition.
Resumen / Abstract Abstract: The transition from a quantum superposition to a definite classical state remains one of the foundational challenges in physics. We propose a dynamical, objective reduction model where wave function collapse is driven by the exchange and dissipation of energy quanta between a quantum system and an observer/environment. Replacing the abstract notion of "measurement" with a physical resolving-rate threshold, we demonstrate that phase coherence decay is directly coupled to the rate of environmentally-emitted quanta capable of resolving the system's spatial superposition. The model is integrated with the Lindblad Master Equation and Stochastic Schrödinger Equations. Numerical evaluations for an isolated electron and a fullerene molecule, validated quantitatively against published thermal decoherence data (Hackermüller et al. 2004), confirm that the corrected model naturally predicts macro-localization on timescales consistent with experiment, while preserving micro-scale quantum superposition — offering a thermodynamically consistent and empirically calibrated boundary for the quantum-classical transition.
The dissipative action threshold postulate (∆Edis · τcollapse ≥ ℏ/2) establishes that objective quantum state reduction is driven by irreversible energy exchange and dissipation with the environment. In this work, we extend the mathematical model to two fundamental applications in applied physics and quantum information: determining thermal fidelity limits in unitary quantum gates and resolving the temporal dynamics and dissipative suppression in quantum tunneling. We derive the maximum allowable environmental radiation density to prevent decoherence in quantum algorithms and demonstrate that the Quantum Zeno Effect emerges naturally as an objective collapse when the dissipative action within a barrier reaches the critical threshold.
This work proposes an objective collapse mechanism in which wave function reduction is triggered when the energy exchanged between a quantum system and a measurement apparatus exceeds a critical threshold Ec. The dynamics is described by an energy-dependent Lindblad master equation that preserves total energy while suppressing coherences above Ec. An interferometric test based on a Mach–Zehnder setup with tunable measurement strength is proposed, predicting a threshold-like loss of visibility. The critical energy can be related to a minimal mass change via E = mc^2, providing an operational link to Penrose–Diósi gravitational collapse scenarios.
We propose a phenomenological model for wave function collapse based on accumulated interaction action (AAA) between a quantum system and its environment. Collapse occurs when the action reaches a critical threshold of order ℏ\hbarℏ, producing a nonlinear sigmoidal transition in coherence. The framework extends open quantum system dynamics and predicts measurable deviations from standard exponential decoherence, such as a "logistic shoulder" in visibility curves. The model is testable in interferometric setups and provides a physically interpretable mechanism for quantum state reduction.