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This research examines how sound speed formulas for degenerate free electron gas behave across different temperatures.

January 22, 2026Open Access

Consistency between the formulas of the sound speed of the degenerate free electron gas at zero and finite temperature

GFG. FaussurierCommissariat à l'Énergie Atomique et aux Énergies Alternatives

Key Points

This research examines how sound speed formulas for degenerate free electron gas behave across different temperatures.
Utilized Sommerfeld expansion for analysis.
Compared sound speed expressions at zero and finite temperatures.
Explored implications for neutron and proton gases.
Demonstrated sound speed expression at finite temperature approaches zero temperature as temperature decreases.
Confirmed consistency in findings for pure neutron and proton gas.
Provided non-trivial insights that enhance previous understanding of sound speed across temperatures.

Abstract

We study the consistency between the formulas of the sound speed of the degenerate free electron gas at zero and finite temperature. Using the Sommerfeld expansion, we show that the expression of the sound speed of the degenerate free electron gas at finite temperature gives the expression of the sound speed of the degenerate free electron gas at zero temperature when the temperature tends to zero at fixed Fermi energy. The present and non-trivial work completes the previous results about the sound speed of the degenerate free electron gas at zero and finite temperature. It is also valid for the pure neutron or proton gas by considering the rest-mass of interest.

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