This repository contains a Mathematica implementation for calculating higher-order derivatives of the thermodynamic pressure in mean-field thermal field theories using a Jacobian-based symbolic approach. The method avoids numerical instabilities associated with finite-difference schemes and provides a robust framework for studying thermodynamic properties in strongly interacting matter.
- Symbolic Derivative Calculation: Automatically handles higher-order pressure derivatives up to any desired order.
- Examples Included:
- Single internal parameter models (e.g., constituent quark mass).
- Two internal parameter models (e.g., constituent quark mass and diquark gap).
- Comparison with Finite-Difference Methods: Demonstrates improved stability and accuracy.
symbolic_pressure_derivatives.nb: The main Mathematica notebook implementing the symbolic calculation of higher-order derivatives in models with one or two internal parameters. Includes:- Examples for calculating coefficients ( c_{mn} ) symbolically.
- Recursive relations for extending to arbitrary orders.
NJL-2f.nb: A Mathematica notebook containing calculations specific to the two-flavor NJL model discussed in the paper. This file includes:- Detailed derivations of pressure derivatives for the two-flavor NJL model.
- Examples tailored to the theoretical framework presented in the paper. These files are complementary to the paper and provides detailed insights and minimal tools for extending the analysis.
- Open the notebook
symbolic_pressure_derivatives.nbin Mathematica. - Follow the instructions in the file to compute specific pressure derivatives for your chosen model.
- For the two-flavor NJL model, refer to the
NJL-2f.nbfile for the detailed derivations and computations. - Customize the symbolic framework for additional constraints or parameters as needed.
M. Hosein Gholami
TU Darmstadt
Email: mohammadhossein.gholami@tu-darmstadt.de
Email: mohogholami@gmail.com