  We consider the Fermi gas in a non-equilibrium state obtained by applying an
arbitrary time-dependent potential to the Fermi gas in the ground state. We
present a general method that gives the quantum statistics of any
single-particle quantity, such as the charge, total energy or momentum, in this
non-equilibrium state. We show that the quantum statistics may be found from
the solution of a matrix Riemann-Hilbert problem. We use the method to study
how the finite measuring time modifies the distribution of the charge
transferred through a biased quantum point contact.
