Thermal Time and Kepler's Second Law

In a fascinating recent paper (arXiv:1302.0724), Haggard and Rovelli (HR) discuss the relationship between the concept of thermal time, the Tolman-Ehrenfest effect and the rate of dynamical evolution of a system - i.e., the number of distinguishable (orthogonal) states a given system transitions through in each unit of time. The last of these is also the subject of the Margolus-Levitin theorem (arXiv:quant-ph/9710043v2) according to which the rate of dynamical evolution of a macroscopic system with fixed average energy (E), has an upper bound ($\nu_{\perp}$) given by:

\begin{equation}
\label{eqn:margolus-levitin}
\nu_{\perp} \leq \frac{2E}{h}
\end{equation}