From MOND entropy to extended uncertainty principles: A unified framework

Abstract

In this study, we explore the relation between generalised entropies and the extended uncertainty principle (EUP) models. Starting from the higher-order extended uncertainty principle (HOEUP), we obtain the modified entropy-area relation. Then, we derive the modified Friedmann equations through three different approaches: the first law of thermodynamics at the apparent horizon, the entropic gravity case, and the emergence of cosmic space. Furthermore, we check the validity of the generalised second law (GSL). Notably, HOEUP modified Friedmann equations are the limiting cases of those obtained from a recently proposed novel entropy, which is derived from Modified Newtonian Dynamics (MOND) [{\it Phys. Dark Universe} {\bf 49} (2025) 101967]. Motivated by this connection, we derive a novel EUP, referred to as MOND EUP, from a reverse procedure. This novel EUP reproduces to EUP relations associated with Rényi and dual Kaniadakis entropies in the limiting cases. Moreover, we show that HOEUP corresponds to perturbative limit of MOND entropy. The main new result of this paper is a reverse procedure beginning from a recently proposed novel MOND entropy to construct a unified EUP. This reverse procedure is not limited with the present case. In principle, the method can be applied to other generalised entropy formalisms, suggesting that our findings may establish a unified framework that bridges the generalised entropies, cutoff mechanisms, and EUP models. In particular, the corresponding modified uncertainty principles may have effective cutoff mechanisms for the entropy forms, which do not explicitly display cutoff mechanisms. Thus, these entropies may have cutoff mechanism due to their corresponding modified uncertainty principles.

15 pages, 1 figure

References in corpus (45)

• On the Origin of Gravity and the Laws of Newton
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• Black hole thermodynamical entropy
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• The Area of a Rough Black Hole
• Dark energy and the generalized second law
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Modified Friedmann Equations from Tsallis Entropy
• Entropic cosmology: a unified model of inflation and late-time acceleration
• Modified cosmology through spacetime thermodynamics and Barrow horizon entropy
• The generalized second law of thermodynamics with Barrow entropy
• Barrow Entropy Corrections to Friedmann Equations
• Generalizing the running vacuum energy model and comparing with the entropic-force models
• GUP Assisted Hawking Radiation of Rotating Acoustic Black Holes
• Modified cosmology through nonextensive horizon thermodynamics
• Extended Uncertainty Principle Black Holes
• Black Hole Remnants in the Early Universe
• Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
• Equipartition of energy and the first law of thermodynamics at the apparent horizon
• Minimal Length, Friedmann Equations and Maximum Density
• The extended uncertainty principle inspires the Rényi entropy
• A note on entropic force and brane cosmology
• Baryon Asymmetry from the Generalized Uncertainty Principle
• Non-singular and Cyclic Universe from the Modified GUP
• Glimpses on the micro black hole Planck phase
• Statistical approaches on the apparent horizon entropy and the generalized second law of thermodynamics
• Corrections to Friedmann equations inspired by Kaniadakis entropy
• Entropic corrections to Friedmann equations and bouncing universe due to the zero-point length
• Primordial Big Bang Nucleosynthesis and Generalized Uncertainty Principle
• The effects of q-statistics on cosmology
• New generalized uncertainty principle with parameter adaptability for the minimum length
• Generalized entropies and the expansion law of the universe
• Modified Friedmann equations from fractional entropy
• Generalized Uncertainty Principle mimicking dynamical Dark Energy: matter perturbations and gravitational wave data analysis
• Modified Friedmann equations from DSR-GUP
• Rainbow gravity corrections to the entropic force
• Investigation of generalised uncertainty principle effects on FRW cosmology
• GUP-Corrected van der Waals Black Holes
• Higher-order generalized uncertainty principle applied to gravitational baryogenesis
• The extended uncertainty principle effects on the phase transitions of Reissner-Nordström and Schwarzschild black holes
• The new higher-order generalized uncertainty principle and primordial big bang nucleosynthesis
• Exponential correction to Friedmann equations
• MOND Theory and Thermodynamics of Spacetime