Developing the Statistical Mechanics of Evolving Assembly Spaces
Abstract
A gap exists in connecting biological evolution within the framework of statistical mechanics. It has been hoped that statistical mechanics would provide us with a general predictive principle for the emergence of novelty and complexity. However, the emergence of novel functional features initiated by stochastic processes remains difficult to describe, because these processes commonly arise outside near-equilibrium or linear-response regimes. To understand how environmental influences generate diverse, open-ended, complex objects by driving physical systems to specific regions of phase space over long spatial and temporal scales, a new approach to non-equilibrium thermodynamics is necessary. Here, we present the coupling of assembly theory (AT) with statistical mechanics as a framework that works within the laws of thermodynamics, but can contextualise the processes of novelty, complexity, and evolution within these laws. We map construction processes from physical space to assembly space (AS) and introduce the concept of an assembler, a machine that constructs objects contingent on previous states and is represented by bitwise operations. Using this approach, we apply principles from stochastic thermodynamics with AT to define selection within large combinatorial spaces1 and estimate the work required to create novel and complex objects. This approach allows us to represent complex processes, such as selection, within large combinatorial spaces as a set of rules for a memory-feedback loop followed by the assembler. This framework concretely defines the relationships between thermodynamics and information theory by introducing a novel aspect of physics that uses history and causal contingency to influence the probabilistic time evolution of complex systems.
Related
BibTeX
@misc{yeddanapudi2026developing,
title = {{Developing the Statistical Mechanics of Evolving Assembly Spaces}},
author = {Anisha K. Yeddanapudi and Abhishek Sharma and Ian Seet and Leroy Cronin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15695},
eprint = {2610.15695},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15695},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Developing the Statistical Mechanics of Evolving Assembly Spaces
AU - Anisha K. Yeddanapudi
AU - Abhishek Sharma
AU - Ian Seet
AU - Leroy Cronin
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15695
UR - https://arxiv.org/abs/2610.15695
AB - A gap exists in connecting biological evolution within the framework of statistical mechanics. It has been hoped that statistical mechanics would provide us with a general predictive principle for the emergence of novelty and complexity. However, the emergence of novel functional features initiated by stochastic processes remains difficult to describe, because these processes commonly arise outside near-equilibrium or linear-response regimes. To understand how environmental influences generate diverse, open-ended, complex objects by driving physical systems to specific regions of phase space over long spatial and temporal scales, a new approach to non-equilibrium thermodynamics is necessary. Here, we present the coupling of assembly theory (AT) with statistical mechanics as a framework that works within the laws of thermodynamics, but can contextualise the processes of novelty, complexity, and evolution within these laws. We map construction processes from physical space to assembly space (AS) and introduce the concept of an assembler, a machine that constructs objects contingent on previous states and is represented by bitwise operations. Using this approach, we apply principles from stochastic thermodynamics with AT to define selection within large combinatorial spaces1 and estimate the work required to create novel and complex objects. This approach allows us to represent complex processes, such as selection, within large combinatorial spaces as a set of rules for a memory-feedback loop followed by the assembler. This framework concretely defines the relationships between thermodynamics and information theory by introducing a novel aspect of physics that uses history and causal contingency to influence the probabilistic time evolution of complex systems.
ER -