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Note: The author acknowledges that in previous publications [43] [44] [45] [46] he relied on the skewing of distributions by quantum statistics and takes this opportunity to correct the record. The quantum statistical examples he used in these papers do not skew the distribution of thermal carriers (unfrozen microstates). However, the CPT symmetrical systems discussed in this paper do. All previously published results relying on statistical skewing still stand when applied to CPT symmetric systems. Asymmetrical statistics can bypass the second law, temperature gradients can form spontaneously. Heat flow in the presence of a magnetic field can have circulation implying that temperature and entropy may not be scalar.

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• 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.