Energy and Parallel Transport (11, 13, 16)

Homotopy theory has a hidden assumption: that strains cost energy. Are uniform solutions n=n0 preferred?

We answer this by considering the form of the continuum free energy density . It must have the properties:

For a material with inversion symmetry, the only good gradient is no gradient. (There is a unique parallel transport on a manifold compatible with the metric and with vanishing torsion...)

This research was paid for by THE US GOVERNMENT by the NSF.

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Last modified: November 2, 1995

James P. Sethna,

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).