#include <deriv_part.h>
The variables dndmu
, dndT
, and dsdT
correspond to
respectively.
All other derivatives can be expressed simply in terms of these three.
Derivatives wrt to chemical potential and temperature:
There is a Maxwell relation
The pressure derivatives are trivial
The energy density derivatives are related through the thermodynamic identity:
Other derivatives:
Note that the derivative of the entropy with respect to the temperature above is not the specific heat, . The specific heat is
To compute the specific heat in terms of the derivatives above, note that the descendants of deriv_part provide all of the thermodynamic functions in terms of and
, so we have
We can then construct a function
and then write the required derivative directly
Now we use the identity
and the Maxwell relation above to give
which expresses the specific heat in terms of the three derivatives which are given.
Note that this is the specific heat per particle, and has no units. If specific heat per unit volume is required, you must multiply by the number density.
No derivative with respect to the bare mass is given, since classes cannot know how to relate the effective mass to the bare mass.
Definition at line 136 of file deriv_part.h.
Data Fields | |
double | dndmu |
Derivative of number density with respect to chemical potential. | |
double | dndT |
Derivative of number density with respect to temperature. | |
double | dsdT |
Derivative of entropy density with respect to temperature. | |
double | dndm |
Derivative of number density with respect to the effective mass. |
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