  We study thermodynamics of entanglement entropy for weakly excited states in
certain non-conformal fields theories, whose gravity duals are given by
non-conformal Dp-branes. We observe that the entanglement entropy of a
sufficiently small system in non-conformal backgrounds still obeys a first-law
like relation, just as the AdS counterparts investigated in arXiv: 1212.1164
[hep-th]. The effective temperature is proportional to the inverse of the size
of the subsystem. The proportionality is a dimensionless constant which is only
determined by the shape of the entangling region and independent of any
coupling. This universality is confirmed by working with the ten-dimensional
string frame metric as well as the lower-dimensional effective metric. When the
entangling region is a strip and translational invariance is broken by metric
fluctuations, we derive a first-law like relation where additional components
of the stress energy tensor are involved.
