MOND Theory and Thermodynamics of Spacetime

TL;DR

This work investigates whether MOND phenomenology can originate from horizon thermodynamics by constructing a MOND-inspired entropy for the apparent horizon. Using this entropy, the authors derive modified Friedmann equations via three thermodynamics–gravity routes: the first law on the apparent horizon, entropic-force arguments, and Padmanabhan’s emergent-space framework. The three approaches yield consistent corrections, including Renyi- and deformed Kaniadakis-like entropy limits and leading-order β corrections, while the generalized second law is preserved on the horizon. Collectively, the results support a thermodynamic origin for MOND and offer a unified framework linking galaxy rotation dynamics to cosmological evolution through horizon thermodynamics.

Abstract

Starting from the Modified Newtonian Dynamics (MOND) theory and using an inverse approach, we construct a general form of the entropy expression associated with the horizon based on the entropic nature of gravity. Using the thermodynamics-gravity correspondence in the cosmological setup, we apply the corrected entropy expression and find the modified Friedmann equation by three methods, namely, (i) the first law of thermodynamics, (ii) the entropic force scenario and (iii) the emergence nature of gravity. We confirm that our model guaranties the generalized second law of thermodynamics for the universe enveloped by the apparent horizon. Our studies reveal that the MOND theory of gravity may be naturally deduced from the modification of the horizon entropy. These results may fill in the gap in the literatures, understanding the theoretical origin of the MOND theory from thermodynamics-gravity conjecture.