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arXiv:2507.04809 · The European Physical Journal Plus

Entropy from decoherence: a case study using Glasma-based occupation numbers

Gabriele Coci, Gabriele Parisi, Salvatore Plumari, Marco Ruggieri

Published Mar 17, 2026• 0 citations

Abstract

Abstract We compute the entropy per particle, S / N , produced by the decoherence of a coherent state interacting with an environment, using an analytical open quantum system approach. The coherent state considered is characterized by occupation numbers borrowed from the Glasma fields produced in the early stages of high-energy nuclear collisions. The environment is modeled as the vacuum, and decoherence arises from the interaction of the state with vacuum fluctuations. We describe the system–environment interaction via a phase-damping model, which represents continuous measurements on the system without altering its energy or particle number. Starting from the occupation numbers typical of the Glasma in high-energy proton–nucleus and nucleus–nucleus collisions, we find that the final S / N after decoherence is lower than that of a two-dimensional thermal bath of ultra-relativistic gluons, except for proton–nucleus collisions at small values of $$g\mu$$ g μ . Our results indicate that quantum decoherence alone does not generate sufficient entropy to transform the initial coherent state into a thermalized gluon bath.

DOI: 10.1140/epjp/s13360-026-07410-4

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Abstract We compute the entropy per particle, S / N , produced by the decoherence of a coherent state interacting with an environment, using an analytical open quantum system approach. The coherent state considered is characterized by occupation numbers borrowed from the Glasma fields produced in the early stages of high-energy nuclear collisions. The environment is modeled as the vacuum, and decoherence arises from the interaction of the state with vacuum fluctuations. We describe the system–environment interaction via a phase-damping model, which represents continuous measurements on the system without altering its energy or particle number. Starting from the occupation numbers typical of the Glasma in high-energy proton–nucleus and nucleus–nucleus collisions, we find that the final S / N after decoherence is lower than that of a two-dimensional thermal bath of ultra-relativistic gluons, except for proton–nucleus collisions at small values of

g\mu

g μ . Our results indicate that quantum decoherence alone does not generate sufficient entropy to transform the initial coherent state into a thermalized gluon bath.

We propose a new prescription for evaluating a von Neumann entropy in the initial stage of high-energy heavy-ion collisions utilizing the time evolution of classical Yang-Mills (CYM) field: The von Neumann entropy is computed for the quantum coherent states constructed so as to give the classical gluon fields as the expectation values. The entropy is to be liberated when the complete decoherence is achieved. As a demonstration, the time evolution of the CYM dynamics is solved with an initial condition which mimics the Glasma state, though in a non-expanding geometry; the Glasma state is characterized by the longitudinal color-electric and -magnetic fields with gluon fields' fluctuations around it. We find that the initial longitudinal fluctuations of the fields play essential roles for the entropy production in two ways: First, the field fluctuations at

t=0

themselves act as a source of the von Neumann entropy prepared before the time evolution. Second, the initial fluctuations triggers field instabilities, and hence the larger the strength of them, the more the entropy production at later time.

We compare decoherence induced in a simple quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We find that even a relatively compact oscillator bath (with the effective number of degrees of freedom of order ten), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case, the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the qubit with the environment.

I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in the usual experimental situations.

Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar fields illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare classical limit can lead to spurious semiquantum chaos, which may affect the determination of entropy production and thermalization also in other cases.

Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar fields illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare classical limit can lead to spurious semiquantum chaos, which may affect the determination of entropy production and thermalization also in other cases.

We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of

J/Ψ

particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.