Debye entropic force and modified Newtonian dynamics

Abstract

Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature $T_D$. The modified entropic force returns to the Newton's law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant $a_0$ involved in MOND is linear in the Debye frequency ${\omega }_D$, which can be regarded as the largest frequency of the bits in screen. We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is taken to be bound of the Universe. The Debye frequency is linear in the Hubble constant $H_0$.

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Cited by in corpus (17)

• MOND theory
• Friedmann equations from emergence of cosmic space
• MOND vs. dark matter in light of historical parallels
• Entropic Force Scenarios and Eternal Inflation
• Noncovariance at low accelerations as a route to MOND
• Entropic gravity, minimum temperature, and modified Newtonian dynamics
• Fundamental Constants, Entropic Gravity and Nonextensive Equipartition Theorem
• Einstein Equations and MOND Theory from Debye Entropic Gravity
• Quantum particle statistics on the holographic screen leads to Modified Newtonian Dynamics (MOND)
• The Effects of Minimal Length in Entropic Force Approach
• Time varying gravitational constant G via the entropic force
• Test of the Law of Gravitation at small Accelerations
• Apparent Dark Matter Inspired by Einstein Equation of State
• Quantized Black Hole and Heun function
• MOND Theory and Thermodynamics of Spacetime
• Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model
• Point-like source solutions in modified gravity with a critical acceleration