  Terahertz (THz) communication is expected to be a key technology for future
sixth-generation (6G) wireless networks. Furthermore, reconfigurable
intelligent surfaces (RIS) have been proposed to modify the wireless
propagation environment and enhance system performance. Given the sensitivity
to blockages and limited coverage range, RIS is particularly promising for THz
communications. Active RIS can overcome the multiplicative fading effect in
RIS-aided communications. In this paper, we explore active RIS-assisted THz
communications. We formulate the ergodic rate, considering factors associated
with active RIS, including active noise and signal amplification, and THz
signals, including molecular absorption and beam misalignment
