Flavor Equilibration
=====================

The flavor equilibration output file, named `charge_neutrality_flavor_equilibration.csv`, serves as input to the  
`Flavor Equilibration <https://gitlab.com/nsf-muses/flavor-equilibration/beta_equil>`_ module. 
To generate the output file, both the **use_charge_neutrality** and **output_flavor_equilibration** options must be enabled, and the files **eos_input_file** and **flavor_equilibration_input_file** must be provided in the config file if you are **not** using the MUSES Calculation Engine.


+---------------------------------------------+------------------+
| **Variable**                                | **Unit**         |
+=============================================+==================+
| Temperature (T)                             | MeV              |
+---------------------------------------------+------------------+
| Baryon chemical potential (:math:`\mu_B`)   | MeV              |
+---------------------------------------------+------------------+
| Strange chemical potential (:math:`\mu_S`)  | MeV              |
+---------------------------------------------+------------------+
| Electron chemical potential (:math:`\mu_e`) | MeV              |
+---------------------------------------------+------------------+
| Baryon density (:math:`n_B`)                | fm\ :sup:`-3`    |
+---------------------------------------------+------------------+
| Strange density (:math:`n_S`)               | fm\ :sup:`-3`    |
+---------------------------------------------+------------------+
| Electric charge density (:math:`n_Q`)       | fm\ :sup:`-3`    |
+---------------------------------------------+------------------+
| Energy density (:math:`\varepsilon`)        | MeV/fm\ :sup:`3` |
+---------------------------------------------+------------------+
| Pressure (:math:`P`)                        | MeV/fm\ :sup:`3` |
+---------------------------------------------+------------------+
| Entropy density (:math:`s`)                 | 1/fm\ :sup:`3`   |
+---------------------------------------------+------------------+
| Proton effective mass (:math:`m_p^*`)       | MeV              |
+---------------------------------------------+------------------+
| Neutron effective mass (:math:`m_n^*`)      | MeV              |
+---------------------------------------------+------------------+
| Proton chemical potential (:math:`\mu_p`)   | MeV              |
+---------------------------------------------+------------------+
| Neutron chemical potential (:math:`\mu_n`)  | MeV              |
+---------------------------------------------+------------------+
| Proton baryon density (:math:`n_p`)         | fm\ :sup:`-3`    |
+---------------------------------------------+------------------+
| Neutron baryon density (:math:`n_n`)        | fm\ :sup:`-3`    |
+---------------------------------------------+------------------+
| Proton optical potential (:math:`U_p`)      | MeV              |
+---------------------------------------------+------------------+
| Neutron optical potential (:math:`U_n`)     | MeV              |
+---------------------------------------------+------------------+

Notice that this differs from the input file:  $\mu_Q$ is replaced by $\mu_e$, and the lepton contribution to energy, pressure and entropy are added.

**Important**: Currently, the Flavor Equilibration module can only handle electrons, so please do not enable any other particles.