Information is not purely abstract. If information is stored in a physical system, destroying that information has thermodynamic consequences.

Our guy Rolf Landauer made this argument in 1961 while studying the physics of computation.

At the logical level, a computer bit has two possible states: 0 or 1. Before looking at the memory, if both states are equally possible, the bit can be either:

0 or 1

There are two possible logical states corresponding to the information.

The information entropy associated with that uncertainty is:

$$ S = k \ln 2 $$

where k is the Boltzmann constant.

Now, let's erase the bit

Imagine we perform an ERASE operation:

$$ \operatorname{ERASE}(x) = 0 $$

That means:

0 -> 0
1 -> 0

So before the operation, the bit could be 0 or 1. After the operation, it can only be 0.

flowchart LR
    A["Before: 0 or 1"] --> B["ERASE"] --> C["After: 0"]

That's a very cool phenomenon: two possible states became one possible state.

This is called logical irreversibility.

Why is that strange or interesting, or cool thing?

To answer that, let's compare it with another computer operation: NOT.