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Can someone help me understand the difference between the Beckenstein bound equations that I’ve come across? They all appear to have different dimensions.

I’ve been told that if you include the Boltzmann constant in the equation, then you’ll have the chemistry version of entropy. Are there different chemistry/physics/information theory values for entropy? $$S_{B} \leq \frac{2 \pi kER}{\hbar c} \\ S_{B} \leq \frac{2 \pi ER}{\hbar c} \\ S_{B} \leq 2 \pi ER.$$

If I’m attempting to determine the information bits (nats) contained within/on a black hole's surface, which would be more appropriate to use?

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  • $\begingroup$ What are $E$ and $R$? Energy and radius of the sphere? $\endgroup$
    – Gabriel Ybarra Marcaida
    Commented Jun 28 at 20:18
  • $\begingroup$ From Wiki: "R is the radius of a sphere that can enclose the given system, E is the total mass–energy including any rest masses." $\endgroup$
    – Nate S
    Commented Jun 28 at 20:20

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They seem to differ only on the choice of units. The second version uses units with $k = 1$ and the last equation uses units with $k = \hbar = c = 1$. These sorts of unit systems are very common in theoretical physics, and sometimes referred to as natural units (depending on which constants are set to $1$).

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