A heterogenetic theory of living systems
Abstract
The problem of the dynamics of living systems and their mathematical representation essentially unfolds on two levels. Firstly, the principles of autopoiesis and operational closure describe how a living system produces and maintains itself. Secondly, living phenomena are recognised as historical, involving the evolution of dynamics and spaces of possibility that change over time. Currently, no differential model can incorporate both of these aspects. We propose adopting the differential heterogenesis framework, which enables us to define differential operators that change in space and time, producing event-based and historical dynamics. In this construction, heterogeneous operator assemblages will be constrained by the principles of autopoiesis and operational closure, providing a theoretical framework for event-based and historical living systems. Finally, we provide a specific example of assembly with Gray-Scott kinetic equations, along with numerical simulations and results.
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BibTeX
@misc{sarti2026heterogenetic,
title = {{A heterogenetic theory of living systems}},
author = {Alessandro Sarti and Giovanna Citti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40524},
eprint = {2610.40524},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40524},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A heterogenetic theory of living systems
AU - Alessandro Sarti
AU - Giovanna Citti
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40524
UR - https://arxiv.org/abs/2610.40524
AB - The problem of the dynamics of living systems and their mathematical representation essentially unfolds on two levels. Firstly, the principles of autopoiesis and operational closure describe how a living system produces and maintains itself. Secondly, living phenomena are recognised as historical, involving the evolution of dynamics and spaces of possibility that change over time. Currently, no differential model can incorporate both of these aspects. We propose adopting the differential heterogenesis framework, which enables us to define differential operators that change in space and time, producing event-based and historical dynamics. In this construction, heterogeneous operator assemblages will be constrained by the principles of autopoiesis and operational closure, providing a theoretical framework for event-based and historical living systems. Finally, we provide a specific example of assembly with Gray-Scott kinetic equations, along with numerical simulations and results.
ER -