# 10.10: J- Thermodynamic Master Equations

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$$E(S, V, N)$$

$$d E=T d S-p d V+\mu d N$$

$$F(T, V, N)=E-T S$$

$$d F=-S d T-p d V+\mu d N$$

$$H(S, p, N)=E+p V$$

$$d H=T d S+V d p+\mu d N$$

$$G(T, p, N)=F+p V$$

$$d G=-S d T+V d p+\mu d N$$

$$\Pi(T, V, \mu)=F-\mu N=-p V$$

$$d \Pi=-S d T-p d V-N d \mu$$

$$p(T, \mu) \text { [intensive quantities only } ]$$

$$d p=\mathcal{S} d T+\rho d \mu \quad[\mathcal{S}=S / V, \quad \rho=N / V]$$

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