Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics

TL;DR

This paper explores how the generalized uncertainty principle (GUP) influences quantum decoherence, revealing connections to Tsallis non-extensive thermostatistics and proposing a new paradigm with potential implications for quantum gravity and analog gravity systems.

Contribution

It derives GUP coherent states linked to Tsallis' probability amplitudes and establishes their equivalence to Tsallis-entropy-based uncertainty relations, introducing a novel framework for quantum decoherence analysis.

Findings

GUP coherent states match Tsallis probability amplitudes in momentum space.

For negative GUP deformation, GUP relates to Tsallis-entropy-power uncertainty relations.

The quasi-classical limit of GUP connects to non-extensive thermostatistics, impacting quantum gravity theories.

Abstract

The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this Letter, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis' probability amplitudes, whose non-extensivity parameter $q$ monotonically increases with the GUP deformation parameter $\beta$. Secondly, for $\beta < 0$ (i.e., $q < 1$), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the Maximal Entropy principle known from estimation theory to reveal connection between the quasi-classical (decoherence) limit of GUP-related quantum theory and non-extensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasi-classical regime has relevant observational consequences. We discuss some of the implications.