  One of the core questions of quantum physics is how to reconcile the unitary
evolution of quantum states, which is information-preserving and
time-reversible, with evolution following the second law of thermodynamics,
which, in general, is neither. The resolution to this paradox is to recognize
that global unitary evolution of a multi-partite quantum state causes the state
of local subsystems to evolve towards maximum-entropy states. In this work, we
experimentally demonstrate this effect in linear quantum optics by
simultaneously showing the convergence of local quantum states to a generalized
Gibbs ensemble constituting a maximum-entropy state under precisely controlled
conditions, while introducing an efficient certification method to demonstrate
that the state retains global purity. Our quantum states are manipulated by a
programmable integrated quantum photonic processor, which simulates arbitrary
non-interacting Hamiltonians, demonstrating the universality of this
phenomenon. Our results show the potential of photonic devices for quantum
simulations involving non-Gaussian states.
