Much work in nonequilibrium statistical mechanics, including stochastic thermodynamics, is based on classical Markov processes that obey local detailed balance. It is well known that such a description follows from assuming the equal-a-priori probability postulate at all time steps, something that was called the "repeated randomness assumption" by van Kampen. Unfortunately, it is also known that the repeated application of the equal-a-priori probability postulate is in blatant contradiction with microscopically reversible Hamiltonian mechanics.
After introducing the problem, I will give an overview of recent analytical and numerical progress that demonstrates how the repeated randomness assumption emerges effectively in an isolated quantum many-body system, provided one focuses on slow and coarse observables of a non-integrable system. If time permits, I will try to highlight various interesting aspects, e.g., the emergence of classicality without environmentally induced decoherence or the existence of multiple different local detailed balance conditions within the same system.