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This study establishes the thermodynamic consistency of the dissipative Diósi-Penrose model by demonstrating that it settles into a non-equilibrium steady-state rather than thermalizing, even under strong dissipation. By moving beyond quadratic approximations with an exact pseudo-spectral simulation, the authors reveal that non-Gaussianity scales with the cube of the dissipation parameter, necessitating advanced numerical methods to capture critical information-theoretic tails. These findings provide a rigorous framework for understanding energy-conserving collapse models and their phase-space dynamics in regimes where perturbative approaches fail.
Non-equilibrium thermodynamics of collapse models in the strongly non-Gaussian regime
arXiv:2606.06259v1 Announce Type: new Abstract: Standard objective collapse models offer a unified approach to the quantum measurement problem but predict an unphysical, indefinite increase in the energy of the system. The dissipative Di\'osi-Penrose (dDP) model resolves this heating issue by introducing a linear friction mechanism. However, this modification induces complex, non-Gaussian phase-space dynamics. We rigorously establish the thermodynamic consistency of this friction mechanism -- extended to the CSL model -- across both weakly and strongly non-Gaussian regimes. Using the Wigner phase-space formalism, we go significantly beyond the quadratic approximation and, to bypass the failure of perturbative methods under strong dissipation, introduce a novel exact pseudo-spectral simulation approach. Our analysis reveals that the system subjected to the dDP mechanism does not thermalize, but rather settles into a non-equilibrium steady-state (NESS) where the asymptotic non-Gaussianity scales as the third power of the dissipation parameter $\beta$. By evaluating the Wigner entropy production, we confirm the thermodynamic validity of the model and demonstrate that highly sensitive information-theoretic quantities require exact numerical methods to accurately capture the key non-Gaussian tails of the distribution.
Abstract:Standard objective collapse models offer a unified approach to the quantum measurement problem but predict an unphysical, indefinite increase in the energy of the system. The dissipative Diósi-Penrose (dDP) model resolves this heating issue by introducing a linear friction mechanism. However, this modification induces complex, non-Gaussian phase-space dynamics. We rigorously establish the thermodynamic consistency of this friction mechanism -- extended to the CSL model -- across both weakly and strongly non-Gaussian regimes. Using the Wigner phase-space formalism, we go significantly beyond the quadratic approximation and, to bypass the failure of perturbative methods under strong dissipation, introduce a novel exact pseudo-spectral simulation approach. Our analysis reveals that the system subjected to the dDP mechanism does not thermalize, but rather settles into a non-equilibrium steady-state (NESS) where the asymptotic non-Gaussianity scales as the third power of the dissipation parameter $\beta$. By evaluating the Wigner entropy production, we confirm the thermodynamic validity of the model and demonstrate that highly sensitive information-theoretic quantities require exact numerical methods to accurately capture the key non-Gaussian tails of the distribution.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2606.06259 [quant-ph]
(or arXiv:2606.06259v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.06259 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 270 words
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