This research specification proposes a numerical test of the constrained ensemble formalism's predicted corrections to the Cardy entropy formula for BTZ black holes. The study aims to derive the constrained partition function for 2D CFTs and verify the predicted correction term α/β² using tensor network simulations (iTEBD/MERA) for c=1/2 and c=1 conformal field theories. The methodology involves computing thermal states via imaginary time evolution, extracting partition functions from correlation functions, and fitting to the predicted functional form. Expected outcomes include measuring the correction coefficient α with <5% uncertainty and distinguishing the constrained formalism from standard holographic thermodynamics.
Key findings
The constrained partition function follows Z_constrained(β) = Z_Cardy(β) × (1 + α/β² + O(β⁻⁴)) where coefficient α is uniquely determined by the constraint structure
The correction term takes the analytical form f_constraint(β, E) ≈ 1 + (πc/3)/(2β²E) + O(β⁻⁴) based on the CFT spectrum
Numerical validation will employ iTEBD with bond dimensions χ = 50-200 for central charges c = 1/2 (Ising) and c = 1 (free boson)
The proposed experiment targets <5% uncertainty in measuring the correction coefficient α to distinguish constrained ensemble from canonical thermodynamics
Limitations & open questions
Study is proposed rather than executed; no empirical data or numerical results are yet available to validate the hypothesis
Finite-size effects and bond dimension limitations in tensor network simulations may obscure the subleading correction signal
The constrained ensemble formalism remains theoretically unverified in black hole contexts and may not produce observable deviations