Discussing a Variational Approach to Electrostatics of Polarizable Heterogeneous Substances

We discuss equilibrium conditions for heterogeneous substances subject to electrostatic or magnetostatic effects.
We demonstrate that the force‐like aleph tensor ℵ and the energy‐like beth tensor ℶ for polarizable
deformable substances are divergence‐free: ∇ = 0 and ∇= 0. We introduce two additional tensors: the
divergence‐free energy‐like gimel tensor ℶ for rigid dielectrics and the general electrostatic gamma tensor Γ
which is not divergence‐free. Our approach is based on a logically consistent extension of the Gibbs energy
principle that takes into account polarization effects. While the model is mathematically rigorous, we caution
against the assumption that it can reliably predict physical phenomena. On the contrary clear models oiien lead
to conclusions that are at odds with experiment and therefore should be treated as physical paradoxes that
deserve the attention of the scientific community. The demand of having simultaneously a logically and
physically consistent theory remains to be the main driving force of progress in thermodynamics. The suggested
approach leads to the mathematically rigorous self-consistent results. Now it has to prove its viability in direct
comparison with experiment. That may prove to be difficult, but real progress is only possible when theory and
experiment challenge each other.