Note: The mobility gradient effect may be familiar to anyone who has driven in winter on a slippery road, lightly covered with snow in the center (because of traffic), and more heavily, near the shoulder. Driving slightly off center, say to the right, increases drag on the right wheels, producing a torque that makes the car veer right, thereby producing more drag on the right wheels. A force is generated perpendicularly to the direction of motion and along the mobility gradient, causing the car to drift quickly and uncontrollably off the icy road and into the snowbank. In this case, there is no magnetic field and the resulting motion occurs along this force.

has been cited by the following article:

• TITLE: Loschmidt’s Paradox, Extended to CPT Symmetry, Bypasses Second Law

  AUTHORS: George S. Levy

  KEYWORDS: Second Law, Boltzmann, Loschmidt, CPT Symmetry, Entropy, Nernst Effect, H-Theorem, Onsager, Paradox, Cross Product

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.12, December 20, 2019

  ABSTRACT: Loschmidt’s paradox is extended by replacing its assumption of time reversibility with full CPT symmetry. Mobility is identified as a means for expressing collisions or dissipation, and the cross product of its gradient with the magnetic field, for expressing parity. Three phenomena incorporating such cross products are identified. The first is the cross product of the mobility gradient with the magnetic field. The second combines this cross product with the E cross B drift. The third is the reciprocal of the Nernst effect expressed as a cross product of the temperature gradient and the magnetic field. Simulations are conducted for testing Loschmidt’s extended paradox. Onsager’s exclusion of magnetic fields and rotation from reciprocals violates CPT symmetry and is unjustified. All three cross-product phenomena skew statistics in a fashion unanticipated by Boltzmann’s assumptions in his H-Theorem. CPT symmetric systems fall outside the assumptions of the theorem which is not rendered invalid but simply limited to its domain of applicability. Therefore, these systems do not violate the second law as Boltzmann defines it. They bypass it.