In this paper we study the first law of thermodynamics for the (2+1) dimensional charged BTZ black hole considering a pair of thermodynamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the right and left movers of string theory and that the temperature associated with the black hole is the harmonic mean of the temperatures associated with these two systems.

PACS numbers: 04.70.Dy, 04.70.Bw, 11.25.–w