Information width: a way for the second law to increase complexity

Many systems appear to increase their “complexity” in time and then robustly maintain a high complexity once achieved [15, 5, 22, 35]. To investigate this phenomenon it is necessary to formalize “complexity”. Here I build on recent work arguing that complexity of a system should be formalized as how much the patterns exhibited on different scales and/or at different locations of that system differ from one another. I quantify this variation in patterns — this type of complexity — as the Jensen Shannon (JS) divergence among the patterns. Next I construct a highly stylized model of off-equilibrium, steady-state, network systems whose structure is maintained by depletion forces. Such networks can be viewed as highly abstracted models of living systems (organisms, ecosystems, or entire biospheres), bypassing considerations of reproduction and natural selection to focus on the underlying physics and information theory. Finally, I show how the second law can drive the growth of these depletion force network systems. I also show that this growth causes such networks to have high JS divergence. In this way the second law can actually drive the increase of complexity in time.

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