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We study the dynamics of a classical circuit corresponding to a discrete-timedeterministic kinetically constrained East model. We show that -- despite beingdeterministic -- this "Floquet-East" model displays pre-transition behaviour,which is a dynamical equivalent of the hydrophobic effect in water. By means ofexact calculations we prove: (i) a change in scaling with size in theprobability of inactive space-time regions (akin to the "energy-entropy"crossover of the solvation free energy in water), (ii) a first-order phasetransition in the dynamical large deviations, (iii) the existence of theoptimal geometry for local phase separation to accommodate space-time solutes,and (iv) a dynamical analog of "hydrophobic collapse". We discuss implicationsof these exact results for circuit dynamics more generally.

Exact "hydrophobicity" in deterministic circuits: dynamical fluctuations in the Floquet-East model