In this case, the posets S and T are said to be order isomorphic. Note that the above definition characterizes order isomorphisms as surjective order embeddings. It should also be remarked that order isomorphisms are necessarily injective. Hence, yet another characterization of order isomorphisms is possible: they are exactly those monotone bijections that have a monotone inverse.
The other is the many-atomic order of statistical mechanics, where ordered states are derived through an appropriate averaging over many interacting particles.
In order to build cells capable of responding adaptively to environmental cues, elaborate signaling networks have evolved capable of reliably, transducing energy from the environment into internal informational states of the cell.
Robustness arises as a byproduct of statistical order in biology as individual components are frequently correlated in their activity, and this can be exploited as a source of redundancy.
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