Complexity of a physical system Are there any accepted definitions quantifying the complexity of:
a) macroscopic, classical mechanical systems (e.g., a bicycle)
b) microscopic systems (ensembles of atoms)?
By the way, I'm not asking about entropy.
References are more than welcome.
 A: I understand that you're not talking about entropy (which is not the same as complexity or disorder), but $\text{complexity}$ is a rather subjective term. I would assume that the relative complexity of a system (which is broad in and of itself, by the way) would have to do with statistical analysis of its parts, the energy required to achieve a certain state, the amount of ways that this state could be acheived, and the apparent function and resilliancy of the state, though there is no known way to accurately quantify something like $\text{complexity}$.
A: Complexity seems like an arbitrary valuation.  There is fundamentally no distinction between microscopic and macroscopic. However, computational complexity is intensely studied and many research groups attempt to bridge the gaps between when classical molecular dynamics and ab initio or ring polymer quantum mechanical simulations are most appropriate.  Here's a sample of coarse graining in biological systems from a collaboration of 4 UChicago profs.
http://pubs.acs.org/doi/abs/10.1021/ct4000444
Hope this helps
A: This is a collection of resources related to complexity.


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*Many physical systems can be represented with graphs:


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*Quantum graphs

*Mechanical systems


*Complexity of a graph or a weighted graph is a notion established by algebraic geometry.


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*http://arxiv.org/abs/0705.2284 (The weighted complexity and the determinant functions of graphs)

*Audrey Terras. Zeta functions of graphs: A stroll through the garden. CUP, 2010.


*Organic chemistry has Wiener index.

*Software development has Cyclomatic complexity.
