Inverted Equation of State output

The output table is written in the format specified by output.format (HDF5 or CSV). Units are set via output.units; the table below shows the natural-unit interpretation. Each entry in the table corresponds to one point on the output grid.

Columns

Whether \(\mu_S/n_S\) and \(\mu_Q/n_Q\) appear in the output mirrors the input.has_S/input.has_Q flags of the table that was inverted (see Equation of State): if a dimension wasn’t in the input table, there’s nothing to solve for or report, so it’s dropped from the output too, not filled with NaN.

Variable	Natural unit	Condition
Temperature (\(T\))	MeV (power 1)	always
Baryon chemical potential (\(\mu_B\))	MeV (power 1)	always
Strange chemical potential (\(\mu_S\))	MeV (power 1)	has_S: true
Electric charge chemical potential (\(\mu_Q\))	MeV (power 1)	has_Q: true
Baryon density (\(n_B\))	MeV3 (power 3)	always
Strange density (\(n_S\))	MeV3 (power 3)	has_S: true
Electric charge density (\(n_Q\))	MeV3 (power 3)	has_Q: true
Energy density (\(\varepsilon\))	MeV4 (power 4)	always
Pressure (\(P\))	MeV4 (power 4)	always
Entropy density (\(s\))	MeV3 (power 3)	always
EoS type index (eos_type)	(integer, see below)	always

Optional columns

The following columns are written only when the corresponding data is present in the input table (and, for the susceptibilities, only when the relevant potential(s) are also present).

Variable	Natural unit	Condition
Heat capacity (\(c_V\))	MeV3 (power 3)	has_heat_capacity: true
Phase index	(dimensionless)	has_phase_index: true
Speed of sound squared (\(c_s^2\))	(dimensionless)	present in input table
Baryon susceptibility (\(\chi_{BB}\))	MeV2 (power 2)	present in input table
Strange susceptibility (\(\chi_{SS}\))	MeV2 (power 2)	present in input table, has_S
Charge susceptibility (\(\chi_{QQ}\))	MeV2 (power 2)	present in input table, has_Q
Mixed susceptibility (\(\chi_{BS}\))	MeV2 (power 2)	present in input table, has_S
Mixed susceptibility (\(\chi_{BQ}\))	MeV2 (power 2)	present in input table, has_Q
Mixed susceptibility (\(\chi_{SQ}\))	MeV2 (power 2)	present in input table, has_S and has_Q
Mixed susceptibility (\(\chi_{TB}\))	MeV2 (power 2)	present in input table
Mixed susceptibility (\(\chi_{TS}\))	MeV2 (power 2)	present in input table, has_S
Mixed susceptibility (\(\chi_{TQ}\))	MeV2 (power 2)	present in input table, has_Q
Temperature susceptibility (\(\chi_{TT}\))	MeV2 (power 2)	present in input table

EoS type index

The eos_type column records which EoS model produced the solution at each grid point. When output.add_eos_index: true, the following integer codes are used:

Index	EoS model
-1	Inversion failed (NaN)
0	Table (primary EoS)
1	Tanh-Conformal
2	Conformal
3	Conformal-Diagonal
4	CD-Modified

Inversion failures

When the root-finder does not converge at a grid point, the behavior is controlled by output.on_inversion_failure:

• nan: The point is kept in the output with thermodynamic fields set to NaN and eos_type = -1. The inversion-target coordinates (grid axis values) are echoed back as-is.

• exclude: The point is dropped from the output entirely. The output dataset will have fewer rows than the full grid.

Output grid structure

The output grid is constructed in the mode specified by grid.mode. See Configuration File for details on explicit and decade modes.