q-generalized Tsallis thermostatistics in Unruh effect for mixed fields

Abstract

It was shown that the particle distribution detected by a uniformly accelerated observer in the inertial vacuum (Unruh effect) deviates from the pure Planckian spectrum when considering the superposition of fields with different masses. Here we elaborate on the statistical origin of this phenomenon. In a suitable regime, we provide an effective description of the emergent distribution in terms of the nonextensive q-generalized statistics based on Tsallis entropy. This picture allows us to establish a nontrivial relation between the q-entropic index and the characteristic mixing parameters sin θ and ∆m. In particular, we infer that q < 1, indicating the superadditive feature of Tsallis entropy in this framework. We discuss our result in connection with the entangled condensate structure acquired by the quantum vacuum for mixed fields.

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

“…Again, we relate the q-index to the mixing angle and the mass difference, in such a way that the standard Fermi-Dirac distribution based on the extensive Boltzmann-Gibbs entropy is restored for vanishing mixing. Similarly to [33], we find a running behavior of q as a function of the energy scale, which is typical for QFT systems [47]. Nevertheless, as opposed to bosons, we now obtain q > 1, that is to say, the entropy function turns out to be subadditive.…”

“…To avoid unphysical divergences, a wavepacket based approach should be performed. This has been done explicitly for bosons in [33,53], where it has been shown that the ensuing spectrum retains the same profile as in the planewave formalism, with the Dirac delta function in energy-momentum being now replaced by the Kronecker delta. However, since wavepackets do not affect the spinorial structure of the field, a similar result is expected to be obtained for fermions as well.…”

“…Nevertheless, as opposed to bosons, we now obtain q > 1, that is to say, the entropy function turns out to be subadditive. Following [33], we explore our result in connection with the entangled condensate structure exhibited by the quantum vacuum for mixed fields.…”

“…The mixing-induced departure of Unruh condensate from the Planckian profile was originally interpreted as a breakdown of the thermality of Unruh effect [29]. In a recent work [33], this result has been revisited in the context of the q-generalized Tsallis statistics based on the nonadditive Tsallis entropy [34][35][36][37]. As well-known, Tsallis entropy is a generalization of the standard Boltzmann-Gibbs definition parameterized by the q-index (in particular, q = 1 corresponds to the nonextensive Tsallis statistics, while q → 1 gives back Boltzmann-Gibbs framework).…”

“…The rationale behind the study of the modified Unruh effect within Tsallis statistics is that the q-generalized entropy well describes systems exhibiting long-range interactions and/or spacetime entanglement, as is the case for mixed fields [31,32,39,40]. In this vein, in [33] it has been shown that the Unruh condensate for mixed particles can still be described as a thermal-like distribution, provided that the underlying statistics is assumed to obey Tsallis's prescription. This picture allows to relate the q-entropic index and the characteristic mixing parameters sin θ and ∆m in a nontrivial way.…”