York's Cavity Formalism and Quantum Modified Thermodynamics of (2+1)D Black Holes

Abstract

We explore the canonical thermodynamics of the non-rotating BTZ black hole within a finite cavity by incorporating quantum corrections using Barrow entropy. We derive analytic expressions for temperature, quasilocal energy, free energy, and specific heat, all evaluated at the cavity boundary by using York's formalism. While the redshifted temperature and energy stay the same despite the entropy changes, the altered entropy affects the thermodynamic landscape. Specifically, we see that the Helmholtz free energy drops faster as the horizon size increases. The specific heat shows clear peaks, and their position and height depend on the Barrow parameter. These features signal enhanced thermal responsiveness and a shift in the onset of black hole dominance. Our results demonstrate that quantum entropy corrections alone, without modifying the geometry, can yield rich thermodynamic behaviour in lower-dimensional gravity and highlight the effectiveness of York's framework in capturing such effects.