  We have studied the specific heat of the $(N_S+N_B)$ model for an $N_S$-body
harmonic oscillator (HO) system which is strongly coupled to an $N_B$-body HO
bath without dissipation. The system specific heat of $C_S(T)$ becomes $N_S
k_B$ at $T \rightarrow \infty$ and vanishes at $T = 0$ in accordance with the
third law of thermodynamics. The calculated $C_S(T)$ at low temperatures is not
proportional to $N_S$ and shows an anomalous temperature dependence, strongly
depending on $N_S$, $N_B$ and the system-bath coupling. In particular at very
low (but finite) temperatures, it may become {\it negative} for a strong
system-bath coupling, which is in contrast with {\it non-negative} specific
heat of an HO system with $N_S=1$ reported by G-L. Ingold, P. H\"{a}nggi and P.
Talkner [Phys. Rev. E {\bf 79}, 061105 (2005)]. Our calculation indicates an
importance of taking account of finite $N_S$ in studying open quantum systems
which may include an arbitrary number of particles in general.
