Abstract
We present a quantitative measure of physical complexity, based on the amount
of information required to build a given physical structure through
self-assembly. Our procedure can be adapted to any given geometry, and thus to
any given type of physical system. We illustrate our approach using
self-assembling polyominoes, and demonstrate the breadth of its potential
applications by quantifying the physical complexity of molecules and protein
complexes. This measure is particularly well suited for the detection of
symmetry and modularity in the underlying structure, and allows for a
quantitative definition of structural modularity. Furthermore we use our
approach to show that symmetric and modular structures are favoured in
biological self-assembly, for example of protein complexes. Lastly, we also
introduce the notions of joint, mutual and conditional complexity, which
provide a useful distance measure between physical structures.
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