WallGo.thermodynamics
Classes that contain thermodynamics quantities like pressure, enthalpy, energy density for both phases
Classes
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Thermodynamic functions corresponding to the effective potential. |
- class Thermodynamics(effectivePotential, nucleationTemperature, phaseLowT, phaseHighT)[source]
Thermodynamic functions corresponding to the effective potential.
All functions can be run outside of the temperature range where the phases exist if the minimum and maximum temperatures of the phases are known (these are obtained by FreeEnergy.tracePhase()) and self.setExtrapolate has been run.
Initialisation
- Parameters:
effectivePotential (EffectivePotential) – An object of the EffectivePotential class.
nucleationTemperature (float) – The nucleation temperature.
phaseLowT (Fields) – The location of the low temperature phase at the nucleation temperature. Does not need to be exact, as resolved internally with input as starting point.
phaseHighT (Fields) – The location of the high temperature phase at the nucleation temperature. Does not need to be exact, as resolved internally with input as starting point.
- Returns:
cls – An object of the Thermodynamics class.
- Return type:
- alpha(T)[source]
The phase transition strength at the temperature \(T\), computed via \(\alpha = \frac{e_{\rm HighT}(T)-e_{\rm LowT}(T) -(p_{\rm HighT}(T) -p_{\rm LowT}(T)) /c^2_{\rm LowT}(T)}{3w_{\rm HighT}(T)}\) as defined in eq. (34) of [GKvdV20]
- Parameters:
T (array-like) – Temperature(s)
- Returns:
alpha – Phase transition strength.
- Return type:
array-like (float)
References
[GKvdV20]F. Giese, T. Konstandin and J. van de Vis, Model-independent energy budget of cosmological first-order phase transitions — A sound argument to go beyond the bag model, JCAP 07 (2020) 07, 057 doi:10.1088/1475-7516/2020/07/057
- csqHighT(temperature)[source]
Sound speed squared in the high-temperature phase, obtained via \(c_s^2 = \frac{dp/dT}{de/dT}\).
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
csqHighT – Sound speed squared in the high-temperature phase.
- Return type:
array-like (float)
- csqLowT(temperature)[source]
Sound speed squared in the low-temperature phase, obtained via \(c_s^2 = \frac{dp/dT}{de/dT}\).
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
csqLowT – Sound speed squared in the low-temperature phase.
- Return type:
array-like (float)
- ddpHighT(temperature)[source]
Second temperature derivative of the pressure in the high-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
ddpHighT – Second temperature derivative of the pressure in the high-temperature phase.
- Return type:
array-like (float)
- ddpLowT(temperature)[source]
Second temperature derivative of the pressure in the low-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
ddpLowT – Second temperature derivative of the pressure in the low-temperature phase.
- Return type:
array-like (float)
- deHighT(temperature)[source]
Temperature derivative of the energy density in the high-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
deHighT – Temperature derivative of the energy density in the high-temperature phase.
- Return type:
array-like (float)
- deLowT(temperature)[source]
Temperature derivative of the energy density in the low-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
deLowT – Temperature derivative of the energy density in the low-temperature phase.
- Return type:
array-like (float)
- dpHighT(temperature)[source]
Temperature derivative of the pressure in the high-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
dpHighT – Temperature derivative of the pressure in the high-temperature phase.
- Return type:
array-like (float)
- dpLowT(temperature)[source]
Temperature derivative of the pressure in the low-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
dpLowT – Temperature derivative of the pressure in the low-temperature phase.
- Return type:
array-like (float)
- eHighT(temperature)[source]
Energy density in the high-temperature phase, obtained via \(e(T) = T \frac{dp}{dT}-p\).
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
eHighT – Energy density in the high-temperature phase.
- Return type:
array-like (float)
- eLowT(temperature)[source]
Energy density in the low-temperature phase, obtained via \(e(T) = T \frac{dp}{dT}-p\).
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
eLowT – Energy density in the low-temperature phase.
- Return type:
array-like (float)
- findCriticalTemperature(dT, rTol=1e-06, paranoid=True)[source]
Computes the critical temperature by finding the temperature for which the free energy of both phases is equal.
- Parameters:
dT (float) – Temperature step size for the determination of Tc
rTol (float, optional) – Error tolerance for the phase tracing
paranoid (bool, optional) – Setting for phase tracing. When True, recomputes minimum at every step
- Returns:
Tc – The value of the critical temperature
- Return type:
float
- pHighT(temperature)[source]
Pressure in the high-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
pHighT – Pressure in the high-temperature phase.
- Return type:
array-like (float)
- pLowT(temperature)[source]
Pressure in the low-temperature phase.
- Parameters:
temperature (array-like) – Temperature(s)
- Returns:
pLowT – Pressure in the low-temperature phase.
- Return type:
array-like (float)
- setExtrapolate()[source]
Allows use of thermodynamics outside of the temperature range where the phase exists. The equation of state gets extrapolated using the template model of [LM15] outside of the allowed range. This function computes the parameters of the template model.
References
[LM15]L. Leitao and A. Megevand, Hydrodynamics of phase transition fronts and the speed of sound in the plasma, Nucl.Phys.B 891 (2015) 159-199 doi:10.1016/j.nuclphysb.2014.12.008
- Return type:
None