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Kelvin State

The Kelvin state is a specific low-temperature phase of liquid crystals characterized by a uniform distribution of molecular orientations, representing a state of maximum entropy.
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The statement of the theorem

Let n0\mathbf{n}_0 be the uniform, constant director vector. The Kelvin state is characterized by the minimization of the free energy functional F[n]F[\mathbf{n}] subject to the constraint of uniform orientation, implying that the order parameter ψ\psi is constant in space and time:\n∂ψ∂t=0,∇ψ=0\frac{\partial \psi}{\partial t} = 0, \quad \nabla \psi = \mathbf{0} \nFurthermore, the free energy density ff must achieve its minimum value fminf_{min} corresponding to the maximum entropy state, such that the elastic energy contribution vanishes:\nF[n]=∫Ωfmind3xF[\mathbf{n}] = \int_{\Omega} f_{min} d^3x
Source: Wikipedia