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