---
# System prepended metadata

title: Bitcoin Mempool vs Black Hole Accretion Disk

---

# Bitcoin Mempool vs Black Hole Accretion Disk

In this short mathematical paper, we will discuss the comparison between the Bitcoin mempool and a black hole accretion disk, as well as the Bekenstein bound and observer's bias.

### Bitcoin Mempool vs Black Hole Accretion Disk
Although the Bitcoin mempool and black hole accretion disk operate in different realms, we can draw a parallel between them using information theory. Let us denote the information density of a system by $I$.

```math
I = \frac{S}{V}
```

Where $S$ is the system's entropy and $V$ its volume. In the case of the Bitcoin mempool, it can be considered as a collection of unconfirmed transactions, while the accretion disk consists of matter orbiting a black hole.

### Bekenstein Bound and Observer's Bias
The Bekenstein bound is a limit on the entropy $S$ of a physical system based on its energy $E$, radius $R$, and the reduced Planck constant $\hbar$.

```math
S \leq \frac{2\pi RE}{\hbar c}
```

Observer's bias can be accounted for by introducing a correction factor $f$:

```math
S_\text{corrected} = fS
```

The corrected entropy allows us to account for the observer's bias and better understand the system's behavior. In summary, while the Bitcoin mempool and a black hole accretion disk are distinct, we can use information theory to draw parallels and investigate their properties with respect to the Bekenstein bound and observer's bias.

<b>References:</b>
<span>[1] <a href='https://docs.github.com/en/get-started/writing-on-github/working-with-advanced-formatting/writing-mathematical-expressions' target='_blank' class='text-purple-1 underline'>Writing mathematical expressions</a></span>
<span>[2] <a href='https://github.blog/2022-05-19-math-support-in-markdown/' target='_blank' class='text-purple-1 underline'>Math support in Markdown</a></span>
<span>[3] <a href='https://jupyterbook.org/content/math.html' target='_blank' class='text-purple-1 underline'>Math and equations</a></span>
