  We study the nonequilibrium steady state of an infinite chain of free
fermions, resulting from an initial state where the two sides of the system are
prepared at different temperatures. The mutual information is calculated
between two adjacent segments of the chain and is found to scale
logarithmically in the subsystem size. This provides the first example of the
violation of the area law in a quantum many-body system outside a zero
temperature regime. The prefactor of the logarithm is obtained analytically
and, furthermore, the same prefactor is shown to govern the logarithmic
increase of mutual information in time, before the system relaxes locally to
the steady state.
