Article: Analysis of absorbed dose in terms of spatial and temporal distribution Journal: International Journal of Nuclear Energy Science and Technology (IJNEST) 2026 Vol.18 No.3 pp.257 - 277 Abstract: The absorbed dose (D) is defined in terms of the imparted energy ε. However, the definition of ε is inconsistent with the rigorous mathematical definition of a stochastic variable. In this study, we evaluate the possible implications of this treatment. To resolve these issues, we analyse the non-stochastic D(r, t) as a function dependent on space and time based on the strict mathematical definition of random and stochastic variables, the fundamentals of linear irreversible thermodynamics (LIT), and the mesoscopic level. An example is presented in reference dosimetry for the determination of the absorbed dose in water, Dw(r, t), through the expected value of the stochastic variable ε(r, t). Here, the temporal dependence of ε(r, t) is eliminated by the charged particle equilibrium condition, considering it as a stationary Markov stochastic process. We present a critical discussion of the previous definitions of D to show how to address the named inconsistencies. Inderscience Publishers - linking academia, business and industry through research

Title: Analysis of absorbed dose in terms of spatial and temporal distribution

Authors: María de los Angeles Montes Rodríguez; Milton Xavier Vargas Verdesoto; Gustavo Alonso; José Trinidad Álvarez Romero

Addresses: Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Av. Instituto Politécnico Nacional, San Pedro Zacatenco, 07738, Mexico City, México; Instituto Nacional de Investigaciones Nucleares, La Marquesa, Ocoyoacac, 52750 Estado de México, México ' Centro Oncológico de Chihuahua, Chihuahua 31217, México ' Instituto Nacional de Investigaciones Nucleares, La Marquesa, Ocoyoacac, 52750 Estado de México, México ' Instituto Nacional de Investigaciones Nucleares, La Marquesa, Ocoyoacac, 52750 Estado de México, México

Abstract: The absorbed dose (D) is defined in terms of the imparted energy ε. However, the definition of ε is inconsistent with the rigorous mathematical definition of a stochastic variable. In this study, we evaluate the possible implications of this treatment. To resolve these issues, we analyse the non-stochastic D(r, t) as a function dependent on space and time based on the strict mathematical definition of random and stochastic variables, the fundamentals of linear irreversible thermodynamics (LIT), and the mesoscopic level. An example is presented in reference dosimetry for the determination of the absorbed dose in water, D_w(r, t), through the expected value of the stochastic variable ε(r, t). Here, the temporal dependence of ε(r, t) is eliminated by the charged particle equilibrium condition, considering it as a stationary Markov stochastic process. We present a critical discussion of the previous definitions of D to show how to address the named inconsistencies.

Keywords: absorbed dose; space and time; imparted energy; stochastic variable; Markov processes; Kolmogorov probability theory; Boltzmann equation; irreversible process thermodynamics; mesoscopic volume.

DOI: 10.1504/IJNEST.2026.154200

International Journal of Nuclear Energy Science and Technology, 2026 Vol.18 No.3, pp.257 - 277

Received: 13 Feb 2026
Accepted: 13 Mar 2026
Published online: 16 Jun 2026 *

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Title: Analysis of absorbed dose in terms of spatial and temporal distribution

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