Algorithmic Mimicry in Physical Processes

• Algorithmic Mimicry is the study of natural and artificial systems that evolve by replicating computational algorithms and matching physical phenomena to defined complexity classes.
• It leverages mathematical models to reinterpret kinetic laws, such as mapping oxidation rates to linear, quadratic, or exponential time complexities.
• This approach informs interdisciplinary strategies, evidenced by shape-memory alloys exhibiting LIFO-like behaviors that bridge concepts from physics and computer science.

Algorithmic mimicry refers to the phenomenon by which natural, artificial, or computational systems evolve, adapt, or operate in a manner that closely replicates algorithmic behavior—executing stepwise procedures, data structuring strategies, or optimization protocols commonly formalized in theoretical computer science. In the context of physical systems, algorithmic mimicry describes the degree to which observed temporal, structural, or behavioral phenomena can be formally mapped to canonical computational paradigms, such as algorithms with well-understood complexity classes or specific data handling rules. This perspective posits that natural processes, far from being arbitrary or purely stochastic, may exhibit intrinsic optimization and information-processing capabilities analogous to digital computation.

1. Recasting Physical Phenomena in Algorithmic Terms

The concept of algorithmic mimicry in physical systems is exemplified by the reinterpretation of empirical laws governing time-evolution in material processes as realizations of algorithmic complexity classes (Pop et al., 2012). The oxidation of metals is a paradigmatic case: instead of relating film thickness (or mass gain, $x$) to elapsed time ($t$), the analysis inverts the relation, focusing on the time required to achieve a particular $x$:

• Parabolic rate law: $t = \frac{x^2 - x_0}{k_p}$, mapped to quadratic time complexity, $\mathcal{O}(n^2)$.
• Logarithmic rate law: $$t = \frac{1}{c} \exp\left(\frac{x}{k_p}\right) - \frac{b}{c}$$, manifesting exponential time complexity.
• Linear rate law: $r = \frac{x}{k_L}$, entailing linear time complexity, $\mathcal{O}(n)$.

This mapping suggests that oxidation kinetics are not arbitrary but may reflect the system’s “choice” of an optimally efficient path under constraints—a selection among “software routines” of different computational costs.

2. LIFO-Like Behavior in Material Transformations

Shape-memory alloys (SMAs) provide a concrete example of material systems mimicking algorithmic data management structures. During deformation and recovery, the sequence of variant formation and de-twinning in martensitic transformations follows a Last-In-First-Out (LIFO) protocol. As stress is applied, distinct microstructural variants are produced; when the stress is released, the last-formed variant reverts first, recapitulating the stack discipline of a standard LIFO data structure.

This analogy is not purely metaphorical: the LIFO ordering ensures recoverability of the initial state through efficient, reversible microstructural transitions, providing both functional robustness and computational tractability. The LIFO paradigm in SMAs thus exemplifies material ordering rules that realize data-structural logic intrinsic to their functional dynamics.

3. Nature as an Intrinsic Optimizer and Computation System

By encoding empirical observations in the formal language of algorithm design and computational complexity, the analysis frames nature’s processes as inherently algorithmic and implicitly optimizing. For oxidation, the governing kinetic law adopted by a system—quadratic, linear, or exponential—can be seen as nature’s selection of an “algorithm” conditioned by physical, chemical, and geometrical constraints to minimize time or resource consumption.

This view posits that at some fundamental level, material evolution and transformation could be interpreted as running computations designed by natural selection for parsimony in time or energy. It suggests a mechanism for the emergence of empirically robust time laws from deeper informational-theoretic or computational constraints, opening the possibility of quantifying the “algorithmic content” of physical laws themselves.

4. Mathematical Formalisms Underpinning Algorithmic Mimicry

Mathematical formalism bridges the physical and computational in this framework. The centerpieces are explicit rate laws—each with unique dependence on the system’s state variable $x$—rendered in LaTeX to clarify their correspondence with classes of computational complexity:

Kinetic Law	Expression	Complexity Class
Parabolic	$t = \frac{x^2 - x_0}{k_p}$	$\mathcal{O}(n^2)$
Logarithmic	$$t = \frac{1}{c}\exp \left( \frac{x}{k_p} \right) - \frac{b}{c}$$	Exponential
Linear	$r = \frac{x}{k_L}$	$\mathcal{O}(n)$

This tabular mapping makes it clear that physical processes are quantifiable in terms familiar from computational theory, equating process time to elementary computational steps and associating physical evolution with discrete algorithmic classes.

5. Implications for Modeling, Control, and Theory Discovery

Viewing physical laws as emergent outcomes of underlying algorithmic processes has substantial implications for scientific modeling and control. Quantitative analogies between time-to-completion and computational step counts may enable the use of performance analysis tools from theoretical computer science to predict or control material evolution. Equally, by monitoring temporal signatures of physical transformations, it may be possible to reverse-engineer the underlying “algorithms” at play, suggesting a pathway for the discovery of new physical laws grounded in algorithmic principles.

This approach also raises the possibility of quantifying the efficiency or “optimality” of existing physical processes—assessing, for instance, whether observed material paths minimize computational resources and whether alternative “algorithms” might be realized through engineered interventions.

6. Broader Significance and Interdisciplinary Connections

Algorithmic mimicry represents a unifying lens linking disparate fields—materials science, physics, computer science, information theory—through the recognition that complex systems, whether natural or artificial, often operate in ways describable by algorithmic concepts. This computational perspective provides a rigorously defined bridge between empirically measurable system dynamics and formal properties of algorithms, extending the reach of algorithmic reasoning well beyond digital computers to the domain of natural phenomena.

In summary, by demonstrating the algorithmic behavior of physical systems such as oxidation kinetics and shape-memory alloys, this framework suggests that algorithmic mimicry is not a superficial resemblance but a potentially fundamental organizing principle. It advocates for analysis, modeling, and discovery in the sciences that leverage algorithmic and computational concepts as intrinsic, not merely analogical, features of reality (Pop et al., 2012).