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Journal of Civil Engineering Research & Technology

Entangled Photon Electron Following Thermo Field Dynamics Method

Ahlem Abidi

Published Nov 30, 2025• 0 citations
Publisher

Abstract

Thermo-field dynamics (TFD) is a method linking quantum information to statistical thermodynamics, focus directly on the state because the states in the tilde space in TFD play a role of tracer of the initial states by defining an extended density matrix described on the double Hilbert space. The study of quantum entanglement is more complicated, so the TFD method makes it easier, this is the subject of this paper. We use Thermo-field Dynamics method to study entanglement entropies and transition probability of a Photon-electron system between equilibrium with heat bath, and non-equilibrium, based on the dissipative von Neumann equation. Numerically, at the equilibrium and by controlling the system through temperature, we show that entanglement entropies verify the Nernst’s theorem. By increasing the quantization of a single-mode electromagnetic field, entanglement and transition probability decrease. At non-equilibrium, we show that entanglement entropies obey the second law of thermodynamics, and the emission of a photon decrease the probability of detecting the electron at a quantum level

DOI
10.47363/jcert/2025(7)193

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Thermo-field dynamics (TFD) is a method linking quantum information to statistical thermodynamics, focus directly on the state because the states in the tilde space in TFD play a role of tracer of the initial states by defining an extended density matrix described on the double Hilbert space. The study of quantum entanglement is more complicated, so the TFD method makes it easier, this is the subject of this paper. We use Thermo-field Dynamics method to study entanglement entropies and transition probability of a Photon-electron system between equilibrium with heat bath, and non-equilibrium, based on the dissipative von Neumann equation. Numerically, at the equilibrium and by controlling the system through temperature, we show that entanglement entropies verify the Nernst’s theorem. By increasing the quantization of a single-mode electromagnetic field, entanglement and transition probability decrease. At non-equilibrium, we show that entanglement entropies obey the second law of thermodynamics, and the emission of a photon decrease the probability of detecting the electron at a quantum level
The quick progress in quantum entanglement research allows us not one to study quantum systems down to N-bodies but also to take a new look at these systems in different branches of physics; particularly the statistical thermodynamics where the application of the thermo-field dynamics (TFD) method to the investigation of entanglement is fruitful. Because the traditional methods based on the identification of a specific parameter show their limit. The process using (TFD) facilitates the understanding of entanglement because it focuses directly on the eigenstate of the system and it is useful in the equilibrium and the non-equilibrium states also. In this context, the (TFD) method is used in this paper to analyze entanglement of an electron interacting with a two-mode electromagnetic field assimilated to an electron with two harmonic oscillators. Entanglement entropies are derived between concerned, not concerned harmonic oscillator and electron compute when the system is in a thermodynamic equilibrium and non-equilibrium state. For the equilibrium case, an increase in the number of particles per unit volume increases the quantum entanglement consequently entanglement appears more important for the couple oscillator-electron than the one electron, this trend is reversed for the non-equilibrium case. By respecting the entanglement parameters, such results allow us to know the relative equilibrium state of the overall system.
We investigate the quantum entanglement of systems of coupled harmonic oscillators on the basis of thermo-field dynamics (TFD). For coupled harmonic oscillators at equilibrium, the extended entanglement entropy is derived using the TFD method, and it is demonstrated to be controlled by temperature and coupling parameters. For non-equilibrium systems, in addition to temperature and coupling parameters, the time dependence of the extended entanglement entropy is calculated in accordance with the dissipative von Neumann equation, and the dissipative dynamics of the systems of coupled harmonic oscillators is discussed. Consequently, based on TFD, the physical parametrization of the entanglement entropies is confirmed in both the equilibrium and non-equilibrium cases of harmonic oscillator systems by means of the laws of thermodynamics.
We study the quantum entanglement of systems of coupled harmonic oscillators on the basis of thermo-field dynamics (TFD).For coupled harmonic oscillators at equilibrium, the extended entanglement entropy is derived using the TFD method, and it is demonstrated to be controlled by temperature and coupling parameters.For non-equilibrium systems, in addition to temperature and coupling parameters, the time dependence of the extended entanglement entropy is calculated in accordance with the dissipative von Neumann equation, and the dissipative dynamics of the systems of coupled harmonic oscillators is discussed.Consequently, based on TFD, the physical parametrization of the entanglement entropies is confirmed in both the equilibrium and nonequilibrium cases of harmonic oscillator systems by means of the laws of thermodynamics.
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We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD). For this purpose, the extended density matrices and extended entanglement entropies of two systems with either non-competing or competing external fields are calculated according to the dissipative von Neumann equation, and the numerical results are compared. Consequently, through the “twin-peaks” oscillations of the quantum entanglement, we have illustrated the Zeeman effect on the entanglement of non-equilibrium finite-spin systems with competing external fields in the TFD algorithm.
We apply a new method based upon thermofield dynamics (TFD) to study entanglement of finite-spin systems with non-competitive external fields for both equilibrium and non-equilibrium cases. For the equilibrium finite-spin systems, the temperature dependence of the extended density matrices is derived using this method, and the effect of non-competitive external field is demonstrated. For the non-equilibrium finite-spin systems, the time dependence of the extended density matrices and the extended entanglement entropies is derived in accordance with von Noumann equation, and the dissipative dynamics of the finite-spin systems is argued. Consequently, the applicability of the TFD-based method to describe entanglement is confirmed in both equilibrium and non-equilibrium cases with the external fieds.