Entropic force versus temperature force

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 ${\vec{F}}_{tem}=m{c}^2(\vec{\nabla }\ln T)$ which leads to the Newtonian force law without introducing the holographic screen defined by holographic principle and equipartition law for entropic force.

10 pages, 2 figures

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