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

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.

arXiv commentManuscript: 6 pages, Supplemental Material: 14 pages

References in corpus (41)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• On the Origin of Gravity and the Laws of Newton
• Lorentz invariance with an invariant energy scale
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Lorentz invariance with an invariant energy scale
• Universality of Quantum Gravity Corrections
• Black hole thermodynamical entropy
• On Gravity and the Uncertainty Principle
• Generalized Uncertainty Principle: Approaches and Applications
• Quantum limit of decoherence: Environment induced superselection of energy eigenstates
• Nonextensive thermodynamic relations
• GUP parameter from quantum corrections to the Newtonian potential
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Pointer states for primordial fluctuations in inflationary cosmology
• Fitting galactic rotation curves with conformal gravity and a global quadratic potential
• Impact of a global quadratic potential on galactic rotation curves
• Generalized Uncertainty Principle and Corpuscular Gravity
• Quantum Theory of Geometry III: Non-commutativity of Riemannian Structures
• On the Decoherence of Primordial Fluctuations During Inflation
• Model for gravity at large distances
• Modified Unruh effect from Generalized Uncertainty Principle
• Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities
• Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies
• The Casimir Effect in Minimal Length Theories based on a Generalized Uncertainity Principle
• Fitting dwarf galaxy rotation curves with conformal gravity
• Observational Constraints on New Exact Inflationary Scalar-field Solutions
• The Coherent State Representation of Quantum Fluctuations in the Early Universe
• Conformal Weyl gravity and perihelion precession
• Generalized uncertainty principles and quantum field theory
• New generalized uncertainty principle from the doubly special relativity
• Solar system constraints on Rindler acceleration
• Heuristic derivation of Casimir effect in minimal length theories
• Pointer states via Decoherence in a Quantum Measurement
• Simple model for quantum general relativity from loop quantum gravity
• Predictability sieve, pointer states, and the classicality of quantum trajectories
• Jeans criterion in nonextensive statistical mechanics
• Universal Properties of Galactic Rotation Curves and a First Principles Derivation of the Tully-Fisher Relation
• Tsallis thermostatics as a statistical physics of random chains
• One-parameter class of uncertainty relations based on entropy power
• The emergence of Special and Doubly Special Relativity
• Rindler type acceleration in f(R) gravity