Did the Big Bang Really Have Low Entropy?

 1. Introduction

We’re often told that the early universe was in a state of "inexplicably low entropy." This idea appears everywhere from textbooks to pop science: it’s the puzzle behind the arrow of time. If entropy always increases, and the future is higher-entropy than the past, then the early universe must have started in a low-entropy state. And low entropy states are highly ordered states, right? Why would the universe have started in a highly ordered state?

2. What is Entropy?

Entropy is often misunderstood as "disorder," but more precisely, it’s a count of how many microscopic states are compatible with the macroscopic conditions of a system. More possible configurations = more entropy.

In a box of gas, high entropy means the particles are spread out randomly, not clustered in a corner. As time passes, the gas tends to spread — not because it’s trying to "disorder" itself, but because there are vastly more ways to be spread out than to be concentrated. Entropy increases not by intention, but by statistics.

3. Why was the Big Bang Hot?

In statistical mechanics, high temperature corresponds to high entropy. If you have a lot of energy in a small volume — as in the early universe — the most probable, highest-entropy state is a hot (smooth?) radiation bath. The energy gets distributed among many short-wavelength, high-energy particles. That’s what high entropy looks like in a small universe.

In other words: the early universe was hot because it was high entropy. In fact, I believe that one could argue that the early universe was at equilibrium -- it had maximum entropy for its size.

4. Then Why Does Entropy Keep Increasing?

Because the universe didn’t stay small. As space expands, it creates more room — not just in a literal sense, but in "phase space", the abstract space of all possible configurations. More volume means more ways particles can be arranged, more available microstates, and thus a higher maximum entropy.

So even if the early universe started with the highest entropy available to it, the expansion of space allowed entropy to keep rising. The second law of thermodynamics doesn’t demand that the early universe was "low" entropy — only that entropy increases from whatever value it started with. And that’s exactly what happened, because space itself was growing.

The growth of "max entropy" due to expansion of space far outpaced the growth of actual entropy, even though both were growing. That gave the universe thermodynamic "elbow room" to undergo processes that unfolded by leveraging the gap -- such as gravitational clumping.

5. Do Clumps Really Have High Entropy?

It’s often said that the early universe was "too smooth," and that a clumpier configuration — with stars and planets already formed — would’ve had higher entropy. But there would seem to be a problem with that idea. In the hot early universe, clumps wouldn’t have lasted. They would have instantly disintegrated under the enormous pressure and thermal motion. Smoothness wasn’t a fragile, special arrangement — it was the stable, high-entropy state under those conditions.

Later, as the universe cooled and expansion made clumping possible, gravitational structures emerged. But that was a change in what kinds of configurations were entropically favored — not a sign that the early universe had been low entropy to begin with. And that change itself was a direct result of the expansion of the universe.

6. Do Black Holes Really Have High Entropy?

The current consensus among physicists today would seem to be that black holes are very highly entropic objects. If that's true, then it would be a mystery why the universe didn't start out as one big black hole, or maybe a collection of smaller black holes.

It could be that the universe was too small at the big bang to mathematically support black holes, or it could be that the universe did start out with black holes but they evaporated -- small black holes evaporate more quickly, and if there were black holes at the big bang, they would have to have been extremely small.

But I think we should be a bit skeptical of the claim that black holes are highly entropic, for reasons I've outlined here: https://mccomplete.blogspot.com/2025/03/do-black-holes-really-have-high-entropy.html

7. The Arrow(s) of Time

Instead of saying "the past is when entropy was lower," maybe we should say something deeper: The past is when space was smaller. The future is when space will be larger. Entropy increases because there’s more room to grow.

First of all, this reduces the "early universe low entropy" problem to the "expanding universe" problem -- a problem we already had. Second of all, it takes two arrows of time -- the thermodynamic arrow and the cosmological arrow -- and unifies them, and argues that the cosmological arrow is more fundamental. In a sense, it reinterprets thermodynamics as geometry.

8. Conclusion

The early universe wasn’t cold and clumpy. It was hot and smooth, and — it would seem to me — typical for a small, newly born universe. As space expanded, entropy increased. The universe of the past was not improbably ordered -- it was just kind of small.