  Numerical methods for the description of nonequilibrium many-particle quantum
systems such as equation of motion techniques often cannot compute the full
statistics of observables but only moments of it, such as mean, variance and
higher-order moments. We employ here the maximum entropy method to numerically
construct unbiased statistics based on the knowledge of moments. We verify the
feasibility of the proposed method by numerical simulation of a simple
birth-death model for quantum-dot-microcavity lasers, where the full photon and
carrier statistics are available for comparison. We show that not only the
constructed statistics but also the computed entropy and the Lagrange
multipliers, which appear here as a byproduct, provide valuable insight into
the physics of the considered system. For example, the entropy reveals that, in
contrast to common wisdom, the photon statistics of the microcavity laser above
threshold is better described by a Gaussian distribution than by a Poisson
distribution. Our approach is general and can be applied to many other systems
emerging in physics and related fields.
