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Whether a thermodynamic potential is “convex upward” or “convex downward” is often important in thermodynamics. In this chapter, we discuss this issue. The topics are the convexities of entropy S[U, V, N], internal energy U[S, V, N], enthalpy H[p; S, N], Helmholtz free energy F[T; V, N], and Gibbs free energy G[T, p; N], Legendre transformation, the concept of natural variables, phase, Gibbs’ phase rule, Duhem’s theorem, and the method to specify the thermodynamic state of a fluid particle.

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Convexity of Thermodynamic Potentials

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  • 发表日期：

    2026年

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  • Takuma Endo

摘要

Whether a thermodynamic potential is “convex upward” or “convex downward” is often important in thermodynamics. In this chapter, we discuss this issue. The topics are the convexities of entropy S[U, V, N], internal energy U[S, V, N], enthalpy H[p; S, N], Helmholtz free energy F[T; V, N], and Gibbs free energy G[T, p; N], Legendre transformation, the concept of natural variables, phase, Gibbs’ phase rule, Duhem’s theorem, and the method to specify the thermodynamic state of a fluid particle.