<p>We develop a unified framework for hybrid generalized uncertainty relations (HGURs) that incorporates two fundamental and competing mechanisms: Planck-scale minimal-length effects encoded by the generalized uncertainty principle (GUP), and the suppression of quantum fluctuations induced by multipartite entanglement as described by generalized uncertainty relations (GURs). Focusing on ensembles of identical pure entangled (IPE) systems, we derive an exact variance-based HGUR valid for an arbitrary number of constituents. The resulting relation reveals a nontrivial interplay between gravity-induced amplification of uncertainty and entanglement-driven redistribution of quantum correlations, leading to an effective reduction of local uncertainties with increasing system size. In the symmetric limit, we identify a critical saturation regime in which the entanglement-induced suppression is exactly balanced by minimal-length corrections, establishing a fundamental bound on the reduction of quantum fluctuations in highly correlated quantum systems. We analyze the limiting behavior of the HGUR and discuss its conceptual implications for the emergence of classical spacetime, as well as potential applications to black hole thermodynamics, inflationary cosmology, and vacuum energy. Our results provide an information-theoretic bridge between quantum gravity effects and the suppression of quantum fluctuations at macroscopic scales.</p>

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Hybrid generalized uncertainty relations from entanglement and minimal length

  • S. Hamid Mehdipour

摘要

We develop a unified framework for hybrid generalized uncertainty relations (HGURs) that incorporates two fundamental and competing mechanisms: Planck-scale minimal-length effects encoded by the generalized uncertainty principle (GUP), and the suppression of quantum fluctuations induced by multipartite entanglement as described by generalized uncertainty relations (GURs). Focusing on ensembles of identical pure entangled (IPE) systems, we derive an exact variance-based HGUR valid for an arbitrary number of constituents. The resulting relation reveals a nontrivial interplay between gravity-induced amplification of uncertainty and entanglement-driven redistribution of quantum correlations, leading to an effective reduction of local uncertainties with increasing system size. In the symmetric limit, we identify a critical saturation regime in which the entanglement-induced suppression is exactly balanced by minimal-length corrections, establishing a fundamental bound on the reduction of quantum fluctuations in highly correlated quantum systems. We analyze the limiting behavior of the HGUR and discuss its conceptual implications for the emergence of classical spacetime, as well as potential applications to black hole thermodynamics, inflationary cosmology, and vacuum energy. Our results provide an information-theoretic bridge between quantum gravity effects and the suppression of quantum fluctuations at macroscopic scales.