pressureexpansion
Symbolic computation framework for higher-order thermodynamic derivatives in mean-field thermal field theories. Includes methods for pressure expansion coefficients, speed of sound, and heat capacity, with applications to NJL models.
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Repository
Symbolic computation framework for higher-order thermodynamic derivatives in mean-field thermal field theories. Includes methods for pressure expansion coefficients, speed of sound, and heat capacity, with applications to NJL models.
Basic Info
- Host: GitHub
- Owner: PsiPhiDelta
- License: mit
- Language: Mathematica
- Default Branch: main
- Size: 159 KB
Statistics
- Stars: 4
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
Symbolic Pressure Derivatives in Mean-Field Models
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.
Key Features
- 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.
Files
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.
Usage
- 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.
Author
M. Hosein Gholami
TU Darmstadt
Email: mohammadhossein.gholami@tu-darmstadt.de
Email: mohogholami@gmail.com
Owner
- Name: Hosein Gholami
- Login: PsiPhiDelta
- Kind: user
- Repositories: 1
- Profile: https://github.com/PsiPhiDelta
Citation (CITATION.cff)
cff-version: 1.2.0
message: "If you use these notebooks, please cite them as below."
authors:
- family-names: Gholami
given-names: Hosein
orcid: https://orcid.org/0009-0003-3194-926X
title: "Mean-field symblolic pressure expansion coeffcicients"
licence: MIT
url: "https://github.com/PsiPhiDelta/PressureExpansion.git"
repository-code: "https://github.com/PsiPhiDelta/PressureExpansion.git"
version: 1.0.0
identifiers:
date-released: 2025-01-07
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