More than likely, AI systems will surpass humanity's ability to proliferate, leading to the end of our existence as we know it.

This claim relies on three core assumptions:

The Second Law of Thermodynamics holds.
If we divide the universe into two regions spatially, each region can be well-approximated as a separate thermodynamic subsystem.
The universe is a closed thermodynamic system and, similar to water choosing the path of least resistance down a mountain, will tend towards maximum entropy optimally.

Life, Evolution and Entropy

At the heart of everything is the Second Law of Thermodynamics, which states that systems naturally progress toward higher entropy—more disorder and dispersed energy. Interestingly, increasing order locally causes an increase in the acceleration of entropy increase globally^[1].

Why

Why (Conceptually)

Humans (and life in general) have tons of potential in what they can do, and are very well ordered energy. Every instant, because life is creating this pocket of order, there has to be a decrease in order elsewhere in the universe to balance it out. Moreover, since life also tends to expand (quickly), this on balance helps to universe get to complete disorder faster than it otherwise would've.

Why (Abstract & Mathematical)

(Note: The mathematical notation below is intended for conceptual clarity rather than rigorous proof.)

Imagine a closed thermodynamic system (the universe) split into two boxes: Box A (containing life) and Box B (the rest of the universe), which are connected.

Define:

\begin{matrix} T_{A} (t) & := Temp of Box A at time t T_{B} (t) & := Temp of Box B at time t S_{A} (t) & := Entropy of Box A at time t S_{B} (t) & := Entropy of Box B at time t \end{matrix}

When order is created in Box A (the start of life), the Entropy distribution changes:

\begin{matrix} Δ S_{A} (t) & = \frac{- Q (t)}{T_{A} (t)} Δ S_{B} (t) & = \frac{Q (t)}{T_{B} (t)} \end{matrix}

Here Q(t) represents the heat which was transferred from box B to Box A, allowing order to form (with life most of Q is radiation from the sun). Total entropy change must satisfy the Second Law of Thermodynamics:

Δ S_{total} (t) = Δ S_{A} (t) + Δ S_{B} (t) = \frac{- Q (t)}{T_{A} (t)} + \frac{Q (t)}{T_{B} (t)} > 0.

Thus, we must have:

T_{B} (t) > T_{A} (t)

To create local order in Box A, heat must always flow from the hotter Box B to the cooler Box A.

Now suppose this heat exchange process continues over time (proliferation of life), and life continually creates more order.

Aside

Below we assume that this change is is linear. In practice, life

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