The core principles of thermodynamics and general relativity provide the
necessary foundation for deriving the polytropic EoS. The first law of thermodynamics asserts a relationship between changes in internal energy U,
work done W, and heat added Q:
dU = δQ − δW.
Polytropic Equation of State in Relativistic Astrophysics
The study of compact astrophysical objects such as neutron stars and white
dwarfs necessitates an understanding of their internal structure and the forces
governing them. As matter is compressed under extreme gravitational fields,
traditional equations of state (EoS) become insufficient.