Dark magnetism revisited

Bacry [Phys. Lett. B 317 (1993) 523] showed that, on the basis of the deformed Poincaré group, special relativity yields a non-additive energy for large systems, i.e., a total energy (of the Universe) which would not be proportional to the number of particles. He consistently argued that this effect could explain (part of) the so-called dark matter. By considering non-interacting spins in the presence of an external magnetic field, it was shown in Portesi et al. [Phys. Rev. E 52 (1995) R3317] that Tsallis’ non-extensive thermostatistics could account for a possible “dark” magnetism (the apparent number of particles being different from the actual one). The work of Pennini et al. [Physica A 258 (1998) 446]; Tsallis et al. [Physica A 261 (1998) 534] uses the so-called “generalized” expectation values, that were for some time considered indispensable in dealing with Tsallis’ formalism. Lately, a different sort of expectation values has been regarded as being superior to the old generalized ones [Pennini et al., Physica A 258 (1998) 446; Tsallis et al., Physica A 261 (1998) 534]. We revisit the dark magnetism question in the light of this new way of computing mean values.