Part I: Foundations

Dissipative Structures and Selection

Introduction
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Dissipative Structures and Selection

A crucial insight is that among the possible structured states, those that persist tend to be those that efficiently dissipate the imposed gradients. This is not teleological; it follows from differential persistence.

We can quantify this. The dissipation efficiency of a structured state A\mathcal{A} measures how much of the available entropy production the state actually channels:

η(A)=σ(A)σmax⁡\eta(\mathcal{A}) = \frac{\sigma(\mathcal{A})}{\sigma_{\max}}

where σ(A)\sigma(\mathcal{A}) is the entropy production rate in state A\mathcal{A} and σmax⁡\sigma_{\max} is the maximum possible entropy production given the imposed constraints. This quantity governs a selection principle: in the long-time limit, the probability measure over states concentrates on high-efficiency configurations:

lim⁡t→∞P(x∈A)∝exp⁡(β⋅η(A))\lim_{t \to \infty} \prob(\mathbf{x} \in \mathcal{A}) \propto \exp\left(\beta \cdot \eta(\mathcal{A})\right)

for some effective selection strength β>0\beta > 0 depending on the noise level and barrier heights.

This provides the thermodynamic foundation for the emergence of organized structures: they are not thermodynamically forbidden but thermodynamically enabled—selected for by virtue of their gradient-channeling efficiency.