  Dynamics of large complex systems, such as relaxation towards equilibrium in
classical statistical mechanics, often obeys a master equation. The equation
significantly simplifies the complexities but describes essential information
of occupation probabilities. A related fundamental question is the
thermalization, a coherent evolution of an isolated many-body quantum state
into a state that seems to be in thermal equilibrium. It is valuable to find an
effective equation describing this complex dynamics. Here, we experimentally
investigate the question by observing sudden quench dynamics of quantum
Ising-like models implemented in our quantum simulator, defect-free single-atom
tweezers in conjunction with Rydberg atom interaction. We find that saturation
of local observables, a thermalization signature, obeys a master equation
experimentally constructed by time-resolved monitoring the occupation
probabilities of prequench states and imposing the principle of the detailed
balance. Our experiment agrees with theories, and demonstrates the detailed
balance in a thermalization dynamics that does not require coupling to baths or
postulated randomness.
