A state of a thermodynamic system which is in thermal, mechanical, and chemical equilibrium.

Specifically it is achieved at:

Maximum Entropy	Minimum Helmholtz free energy	Minimum Gibbs Free Energy
$\begin{array}{l}S \rightarrow \rm max\end{array}$	$\begin{array}{l}A(T, V) \rightarrow \rm min\end{array}$	$\begin{array}{l}G(p, T) \rightarrow \rm min\end{array}$
for isolated system	for a system with $\begin{array}{l}T = {\rm const} , \ V = {\rm const}\end{array}$	for a system with $\begin{array}{l}p = {\rm const} , \ T = {\rm const}\end{array}$

Particularly in Fluid Dynamics it means that:

(1)	$\begin{array}{l}\displaystyle G \rightarrow \rm min \ \Leftrightarrow \mathrm{d}G = 0\end{array}$

The Gibbs free energy is at minimum

(2)	$\begin{array}{l}\displaystyle T= \rm const\end{array}$

the fluid temperature is constant at any moment of time $\begin{array}{l}t\end{array}$ and spatial location $\begin{array}{l}{\bf r} = (x,y,z)\end{array}$ of a fluid flow

(3)	$\begin{array}{l}\displaystyle p=\rm const\end{array}$

the fluid pressure is constant at any moment of time $\begin{array}{l}t\end{array}$ and spatial location $\begin{array}{l}{\bf r} = (x,y,z)\end{array}$ of a fluid flow

(4)	$\begin{array}{l}\displaystyle \rho = \rho(p, T)=\rm const\end{array}$

fluid density is a function of pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ only

(5)	$\begin{array}{l}\displaystyle \mu = \mu(p, T)=\rm const\end{array}$

fluid viscosity is a function of pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ only

(6)	$\begin{array}{l}\displaystyle \lambda = \lambda(p, T)=\rm const\end{array}$

fluid thermal conductivity is a function of pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ only

(7)	$\begin{array}{l}\displaystyle c_p = c_p(p, T)=\rm const\end{array}$

fluid isobaric specific heat capacity is a function of pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ only

(8)	$\begin{array}{l}\displaystyle \alpha = \alpha(p, T)=\rm const\end{array}$

fluid Joule–Thomson coefficient is a function of pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ only

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See also

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Thermodynamic equilibrium

See also