  This paper discusses the thermodynamic properties for certain time-dependent
dynamical systems. In particular, we are interested in time-dependent dynamical
systems with the specification property. We show that each time-dependent
dynamical system given by a sequence of surjective continuous self maps of a
compact metric space with the specification property has positive topological
entropy and all points are entropy point. In particular, it is proved that
these systems are topologically chaotic. We will treat the dynamics of
uniformly Ruelle-expanding time-dependent dynamical systems on compact metric
spaces and provide some sufficient conditions that these systems have the
specification property. Consequently, we conclude that these systems have
positive topological entropy. This extends a result of Kawan \cite{K2},
corresponding to the case when the expanding maps are smooth, to the more
general case of expanding maps. Additionally, we study the topological pressure
of time-dependent dynamical systems. We obtain conditions under which the
topological entropy and topological pressure of any continuous potential can be
computed as a limit at a definite size scale. Finally, we study the Lipschitz
regularity of the topological pressure function for expansive (uniformly
Ruelle-expanding) time-dependent dynamical systems on compact metric spaces.
