Quantifying the Complexity of Materials with Assembly Theory (2502.09750v2)

Abstract: Quantifying the evolution and complexity of materials is of importance in many areas of science and engineering, where a central open challenge is developing experimental complexity measurements to distinguish random structures from evolved or engineered materials. Assembly Theory (AT) was developed to measure complexity produced by selection, evolution and technology. Here, we extend the fundamentals of AT to quantify complexity in inorganic molecules and solid-state periodic objects such as crystals, minerals and microprocessors, showing how the framework of AT can be used to distinguish naturally formed materials from evolved and engineered ones by quantifying the amount of assembly using the assembly equation defined by AT. We show how tracking the Assembly of repeated structures within a material allows us formalizing the complexity of materials in a manner accessible to measurement. We confirm the physical relevance of our formal approach, by applying it to phase transformations in crystals using the HCP to FCC transformation as a model system. To explore this approach, we introduce random stacking faults in closed-packed systems simplified to one-dimensional strings and demonstrate how Assembly can track the phase transformation. We then compare the Assembly of closed-packed structures with random or engineered faults, demonstrating its utility in distinguishing engineered materials from randomly structured ones. Our results have implications for the study of pre-genetic minerals at the origin of life, optimization of material design in the trade-off between complexity and function, and new approaches to explore material technosignatures which can be unambiguously identified as products of engineered design.

• The paper extends Assembly Theory (AT) to quantify the complexity of inorganic materials like crystals and minerals, using an assembly index (ai) measuring construction steps.
• The methodology analyzes unit cells via hierarchical decomposition and assembly index, showing varied complexity in natural materials and higher levels in engineered structures.
• This framework has implications for understanding material genesis, optimizing material design, identifying engineered 'technosignatures', and potential future AI applications.

Assembly Theory Applied to Quantifying Material Complexity

This paper advances the application of Assembly Theory (AT) to the domain of inorganic materials, focusing on their complexity by expanding AT's principles to include crystalline and engineered solid-state objects. The researchers outline a methodology to empirically measure complexity, distinguishing naturally occurring materials from engineered ones through the concept of assembly.

Extending Assembly Theory to Inorganic Systems

The authors extend AT's framework to quantify the complexity of inorganic molecules and solid-state structures like crystals, minerals, and microprocessors. Fundamental to this is the assembly index (ai), a measurement detailing the minimum steps required to construct an object from its elemental units. The paper presents the quantification of this index, for instance, by analyzing the hexagonal close-packed (HCP) to face-centered cubic (FCC) phase transformation model. This demonstrates how AT can detect variations in complexity through stacking faults and crystalline transformations.

Methodological Framework and Numerical Insights

The approach utilizes hierarchical decomposition to dissect materials into unit cells, which are then analyzed for their assembly indices. For detailed analysis, procedures included a comparison of unit cell assembly indices across diverse mineral structures via a database of crystal structures. The findings corroborated that naturally occurring unit cells exhibit varied complexity levels, determined by bond heterogeneity and structural disorder. Additionally, these scenarios highlight how assembly contributes towards understanding micro to macro-structural complexities.

Implications for Material Science

The paper's analysis shows its applicability to areas like the genesis of life, optimization in material design, and the identification of engineered materials. The concept of technosignatures is introduced, applying the framework to strictly engineered materials, such as CMOS chips, which highlight the ability to identify structures beyond natural complexity thresholds. By showcasing geometrical arrangements and defect densities, it confirms engineered settings possess higher complexity due to intentional design constraints.

Future Directions and Conclusion

The framework not only paves the way for deeper exploration in material technosignatures but also offers potentials in optimizing materials for desired properties through a quantitative understanding of complexity. This paper sets the foundation for integrating AT into analyzing real-time dynamic processes, thereby offering promising avenues for future AI-facilitated investigations in material science.

Overall, this research provides crucial insights into assembly theory's role in quantifying material structures, presenting implications across disciplines from evolutionary biology to cutting-edge materials engineering. As the field advances, assembly theory could become a core tool in modeling and synthesizing complex inorganic materials.