Entropic force versus temperature force

TL;DR

This paper introduces a temperature force derived from the Tolman temperature in stationary spacetime, showing it can reproduce Newtonian gravity without holographic assumptions.

Contribution

It presents a novel derivation of Newtonian force from temperature gradients using relativistic thermodynamics, bypassing holographic principles.

Findings

Temperature force matches Newtonian gravity.

Non-relativistic temperature derived from Tolman temperature.

Force expression involves gradient of logarithmic temperature.

Abstract

We introduce the cavity enclosing a source mass $M$ to define the temperature force. Starting with the Tolman temperature in the stationary spacetime, we find a non-relativistic temperature $T_{non}= T_\infty(1-\Phi/c^2)$ with the Newtonian potential $\Phi$. This temperature could be also derived from the Tolman-Ehrenfest effect, satisfying a relation of $T=T_{\infty}e^{-\Phi/c^2}$ with the local temperature $T$. Finally, we derive the temperature force $\vec{F}_{tem}=mc^2(\vec{\nabla} \ln T )$ which leads to the Newtonian force law without introducing the holographic screen defined by holographic principle and equipartition law for entropic force.