Herein, we extend Joule-Thomson expansion to the low-dimensional regime by considering the rotating Bañados-Teitelboim-Zanelli (BTZ) metric in the ($2+1$)-dimensional space-time. Specifically, the properties of three important aspects of the Joule-Thomson expansion, including the Joule-Thomson coefficient, inversion curve, and isenthalpic curve were studied. The divergence point of the Joule-Thomson coefficient and the zero point of the Hawking temperature were investigated. The inversion temperature and isenthalpic curves in the $T–P$ plane were obtained, and the cooling-heating regions were determined. Furthermore, the minimum inversion temperature was found to be zero, and the black hole becomes an extremal black hole. The ratio of the minimum inversion and critical temperatures for BTZ black holes does not exist, since the BTZ black hole does not exhibit the critical behavior in the critical pressure $P_c$, critical temperature $T_c$, and critical volume $V_c$.

• Received 26 May 2021
• Accepted 24 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.124003