Motivation
Exact canonical-ensemble calculations (Fourier/Bessel-sum style) can become slow and/or numerically unstable for large volumes and/or large conserved charges. A saddle-point (steepest-descent) treatment provides a fast, controlled large-V approximation with a well-defined NLO correction (Gaussian prefactor), and can serve as a practical alternative in regimes where exact CE is expensive.
Proposal
Add canonical-ensemble calculations using a saddle-point approximation:
- LO: exponent evaluated at the saddle point (Legendre-transform style)
- NLO: Gaussian prefactor from the Hessian (determinant of susceptibility matrix)
Support a configurable subset of conserved charges to be treated canonically (e.g. S only; or B,Q,S; optionally C).
Implement as a flag in existing ThermalModelCanonical class, or in a derived class ThermalModelCanonicalSaddlePoint.
Motivation
Exact canonical-ensemble calculations (Fourier/Bessel-sum style) can become slow and/or numerically unstable for large volumes and/or large conserved charges. A saddle-point (steepest-descent) treatment provides a fast, controlled large-
Vapproximation with a well-defined NLO correction (Gaussian prefactor), and can serve as a practical alternative in regimes where exact CE is expensive.Proposal
Add canonical-ensemble calculations using a saddle-point approximation:
Support a configurable subset of conserved charges to be treated canonically (e.g.
Sonly; orB,Q,S; optionallyC).Implement as a flag in existing ThermalModelCanonical class, or in a derived class ThermalModelCanonicalSaddlePoint.