<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi></mml:math>-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 $\mathrm{sin}\ensuremath{\theta}$ and $\mathrm{\ensuremath{\Delta}}m$. 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.