  Understanding equilibration and thermalization in isolated many-body quantum
systems is a central challenge in quantum physics. The traditional approach
focuses on the study of the full state of the quantum system which, at
equilibrium, is best described by the Diagonal Ensemble. Here, we present
Observable Statistical Mechanics, a novel paradigm that shifts attention from
the full quantum state to the statistics of measurement outcomes. This approach
is grounded in the Maximum Observable Entropy Principle, positing that
equilibrium measurement statistics tend to maximize observable entropy under
conserved average energy. By focusing on accessible measurements, the theory
accurately predicts equilibrium probability distributions without needing
detailed microscopic information like the energy eigenstates. Extensive
numerical experiments on 7 spin-1/2 Hamiltonians demonstrate the broad
applicability and robustness of this framework.
