= Free-energy density
{title2=$f$}
{wiki}
A <free-energy density> is <free energy> per unit <volume>, with units of <pressure> or <energy density>. For a homogeneous state, $F=Vf$ when surface contributions are neglected. A function $f(\phi,T)$ of an <order parameter> compares the thermodynamic cost of candidate uniform states at a fixed <temperature>.
For example, $f=f_0+a\phi^2/2+b\phi^4/4$ with $b>0$ has a minimum at $\phi=0$ when $a>0$, and minima at $\phi=\pm\sqrt{-a/b}$ when $a<0$. This is a simple <Landau theory> description of a change in preferred state. Stability requires the appropriate constrained minimum: a conserved total <order parameter> or coexistence of phases changes the minimization problem. A spatially varying field additionally requires gradient and boundary terms, so minimizing only a local <free-energy density> cannot determine an interface profile.
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