The Many Faces of Torsion

At least six definitions of ''torsion'' appear in the physics literature complicating the utilization and understanding of the concept. In this article, the differences and similarities of the various definitions are compared, and their relationships to spaces of absolute parallelism with applications to irreversible thermodynamics, coherent structures in plasmas and fluids, and general relativity are described.

In the download pdf file (see below) the concept of torsion and torsion fields are investigated. There are at least six different definitions of torsion to be found in the literature. They include:

  • The Frenet Torsion of a space curve.
  • The Frenet Helicity Torsion of a Bernoulli fluid flow.
  • The Torsion described by the anti-symmetric components of a Cartan right connection.
  • The Torsion described by the anti-symmetric components of a Cartan left connection.
  • The Cartan Torsion 2-forms.
  • The Topological Torsion of a 1-form.

Topological Torsion is the concept of highest interest to this web site. If the 1-form of heat, Q, has zero topological torsion, then the process that created the heat 1-form is thermodynamically reversible.

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Last update 08/27/2001
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