  We study a relativistic fluid with longitudinal boost invariance in a
quantum-statistical framework as an example of a solvable non-equilibrium
problem. For the free quantum field, we calculate the exact form of the
expectation values of the stress-energy tensor and the entropy current. For the
stress-energy tensor, we find that a finite value can be obtained only by
subtracting the vacuum of the density operator at some fixed proper time
\tau_0. As a consequence, the stress-energy tensor acquires non-trivial quantum
corrections to the classical free-streaming form.
