Space-Time Duality of Diffusion via Subordination: General Theory and Relativistic Models
Abstract
The Cattaneo-Vernotte model and the relativistic Schrödinger operator represent two fundamental frameworks for the relativistic modifications of normal diffusion, leading to the telegraph equation and a class of spatially nonlocal diffusion equations, respectively. This paper investigates the intrinsic connection between these two relativistic diffusion models. While it is well-established that spatially non-local diffusion arises from subordinating normal diffusion, we reveal a novel reciprocal mechanism: the normal diffusion process can be recovered by subordinating the telegraph process via the corresponding inverse subordinator. Consequently, leveraging the duality between the subordinator and the inverse subordinator, we establish a distinct duality between the telegraph equation and the spatially nonlocal diffusion equation. Furthermore, this specific duality, centered on normal diffusion, is generalized to a broader class of space-time dual operator families anchored on C0-semigroups.
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BibTeX
@misc{li2026spacetime,
title = {{Space-Time Duality of Diffusion via Subordination: General Theory and Relativistic Models}},
author = {Cheng-Gang Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.04270},
eprint = {2606.04270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04270},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Space-Time Duality of Diffusion via Subordination: General Theory and Relativistic Models
AU - Cheng-Gang Li
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2606.04270
UR - https://arxiv.org/abs/2606.04270
AB - The Cattaneo-Vernotte model and the relativistic Schrödinger operator represent two fundamental frameworks for the relativistic modifications of normal diffusion, leading to the telegraph equation and a class of spatially nonlocal diffusion equations, respectively. This paper investigates the intrinsic connection between these two relativistic diffusion models. While it is well-established that spatially non-local diffusion arises from subordinating normal diffusion, we reveal a novel reciprocal mechanism: the normal diffusion process can be recovered by subordinating the telegraph process via the corresponding inverse subordinator. Consequently, leveraging the duality between the subordinator and the inverse subordinator, we establish a distinct duality between the telegraph equation and the spatially nonlocal diffusion equation. Furthermore, this specific duality, centered on normal diffusion, is generalized to a broader class of space-time dual operator families anchored on C_0-semigroups.
ER -