Parameters

The 4D Taylor-expansion lattice (BQS) equation of state module has a variety of parameters for the calculation of the equation of state. The output file will correspond to the selected parameter choices.

As described in the Quickstart, the user must provide a config.yaml file. The purpose of this file is to supply all the configuration information required to run the module, such as input data and program options. The rules for this input file are specified in the OpenAPI 3.0.0 Specifications file provided with the module.

Each time the module is executed, it reads the config.yaml file provided by the user and verifies that the input conforms to the OpenAPI specifications. If it does not, module execution will be unsuccessful. When this happens, make sure to check the logs to identify the issue with your configuration.

It is not necessary to specify every single parameter in the configuration file. If any parameter is omitted, it will be automatically assigned its default value. The default values for each parameter can be found in the OpenAPI specification.

Upon successful execution, the module may produce several output files. These are described in the OpenAPI specification as part of the output schema. Not all of these files are created during every run, and some require the user to specify particular options in the config.yaml file.

Below are tables providing a brief overview of module’s input, semi-internal and output parameter files. These include parameter names, default values, and descriptions similar to those in the OpenAPI specification file for the module.

Input Parameters

The input parameters required to execute the BQS module are presented in the table below. All parameters have default values in case the user does not specify any. Complete details are given in the module’s OpenAPI specifications.

Category Description	Input Parameter	Default	Description
Grid	`T_min`	`30.0`	Minimum temperature (in `MeV`)
	`T_max`	`600.0`	Maximum temperature (in `MeV`)
	`dT`	`5.0`	Step size in temperature (in `MeV`)
	`mu_B_min`	`0.0`	Minimum baryon chemical potential (in `MeV`)
	`mu_B_max`	`450.0`	Maximum baryon chemical potential (in `MeV`)
	`dmu_B`	`5.0`	Step size in baryon chemical potential (in `MeV`)
	`mu_Q_min`	`0.0`	Minimum electric charge chemical potential (in `MeV`)
	`mu_Q_max`	`450.0`	Maximum electric charge chemical potential (in `MeV`)
	`dmu_Q`	`5.0`	Step size in electric charge chemical potential (in `MeV`)
	`mu_S_min`	`0.0`	Minimum strange chemical potential (in `MeV`)
	`mu_S_max`	`450.0`	Maximum strange chemical potential (in `MeV`)
	`dmu_S`	`5.0`	Step size in strange chemical potential (in `MeV`)

Following is an example of a typical config.yaml for the BQS module:

parameters:
  T_min: 30
  T_max: 50
  dT: 5
  mu_B_min: 0
  mu_B_max: 10
  dmu_B: 5
  mu_Q_min: 0
  mu_Q_max: 10
  dmu_Q: 5
  mu_S_min: 0
  mu_S_max: 10
  dmu_S: 5
switchers:
  get_P: True
  get_s_dens: True
  get_B_dens: True
  get_Q_dens: True
  get_S_dens: True
  get_E_dens: True
  get_c_s: True
  get_P_derivatives_finite_mu: True
  get_Chis_zero_mu: True
  get_dChisdT_zero_mu: True
  get_d2ChisdT2_zero_mu: True

Semi-internal variables

The input parameters required to run the BQS equation of state are the coefficients \(a_{0-9}\), \(b_{0-9}\) and \(c_0\) of the parameterization used to obtain the lattice-based susceptibilities, as explained in the Physics overview.

The default value of these parameters are obtained from reference [1]. They are stored in REF-BQS_eos_input_coef.yaml, an auxiliary input file placed in the test/Ref_files/ repository. In principle, one can update the values of the coefficients based on a similar fit to new lattice data. To do so, one can either simply change this same file as is, or place the resulting file, without the “REF-” prefix, in the input/ repository, and execute the module by calling this input file after the config.yaml file. Since this file is not required to run the module, the coefficients will be read from the “REF-” file by default.

Output Parameters

The output files generated by the module are in .csv format, and are stored in the output/ directory, assuming they have to be produced according to the different switchers.

BQS_eos_output_thermodynamics.csv: this file contains values for thermodynamic observables such as pressure, energy density, charge densities, entropy density or second-order derivatives of pressure, as a function of temperature \(T\) and the conserved charge chemical potentials, i.e. \(\mu_B\), \(\mu_Q\) and \(\mu_S\).

BQS_eos_output_chis.csv: this file contains the values of all susceptibilities of \(0^{th}\), \(2^{nd}\) and \(4^{th}\) order used in the construction of the EoS, as a function of the chosen temperature grid, at zero chemical potentials only.

References