The universe and your morning coffee

The universe and your morning coffee

coffee, entropy and complexity

In a closed system, like the universe, entropy can only stay the same or increase over time. And yet we see rich complexity emerge, both here on Earth (including life itself!) and across the cosmos. How does this apparent order emerge in a system with increasing entropy? The answer lies in your morning coffee.

Last year I attended a lovely public lecture by physicist Sean Carroll, drawing from his recent book The Big Picture. In the lecture (and the book) he poses the following question, recast in my own meandering way:

How did complexity arise in the cosmos (solar systems to galaxies to galactic clusters) and here on earth (intricate weather patterns, life itself) when the universe, as a whole, is a closed system?

A closed system is one in which no energy can be added or removed. In a closed system, the total entropy can only stay the same or increase. This principle is known as the Second Law of Thermodynamics and it forms the bedrock of our understanding of physics and the way the universe functions. It’s as incontrovertible and unassailable as physical laws can get.

It’s THE Law.

(And scientists in general do not throw around the word “Law” lightly.)

A creature like yourself is a highly ordered system, complex and intricate. Your entropy is low. And yet you arose in a universe that is a closed system. There is an apparent contradiction at play. So what is the resolution?

I’m often reminded of the answer as I prepare my morning coffee.

Entropy and my living room

First let’s form a clearer picture of what entropy actually means. We’ll start in my living room.

My husband bought our son a fantastic, giant set of foam building blocks. Here’s one of the pictures they advertise with:

Building made of foam blocks.
A rough approximation for the delightful structures my 11 month old builds. Ha.

That building in front of the boy can exist in just one configuration. If you start swapping the positions of the blocks, you end up with a different building. Perhaps it just varies in color, perhaps the swap would cause the whole thing to collapse. If the number of configurations in which you can have a “state” (in this case, the state of the blocks is “the building”) is low, then its entropy is low. Entropy is low in ordered systems.

Now let’s let the arrow of time progress. Invariably, our living room ends up looking more like this:

Foam blocks in a pile.
Alex channeling his inner architect.

There are many many ways in which foam blocks can exist in the state “pile”. In my living room we explore the various permutations daily. If we swap the positions of two blocks, the pile is still a pile. If the number of configurations in which you can have a “state” is high, then its entropy is high. Entropy is high in disordered systems.

So as time progresses, if I put no work into the living room (ie, useful energy–the kind it takes to clean up), then a building is very likely to form a pile, since there are many ways to construct a pile. But my pile is unlikely to fall into a building, as there’s only one way to end up as a building.

Since building a structure involves fighting gravity, which definitely involves adding work, let’s consider a slightly better analogy. If you drop pieces of a jigsaw puzzle onto a table, they are very likely to land in a pile of puzzle pieces and very unlikely (though it’s not impossible) to land configured as the completed puzzle. It’s just a simple question of probability. There are nigh uncountable configurations* for a pile of puzzle pieces, but only one configuration for a completed puzzle. The odds just aren’t with you.

The universe in a cup of coffee

So back to my morning coffee. When I first brew my cup, I have a low entropy, lovely dark brew. It’s all coffee and water, homogeneous. If you swap out two molecules, they’re both identical, so you end up with the same configuration of coffee. Low number of configurations, low entropy.

Black coffee is homogeneous and low entropy.
Lovely dark and deep. Black coffee is homogeneous and low entropy.

But I like my coffee like I like my men, pale and weak. (My husband never gets tired of that joke. Har har.) After I add in a little milk, my coffee becomes a heterogeneous blend of milk molecules and coffee. Now the entropy in my cup is high–there are many ways to swap around milk and coffee molecules, but they would all taste the same. And it would take a lot of work to separate out the milk molecules from the coffee again!

Coffee with milk is heterogeneous and high entropy.
Coffee with milk is heterogeneous and high entropy.

Things only get interesting in the intermediate state, as I’m pouring in the milk. Here we see rich complexity–plumes of milk forming intricate patterns that evolve in time. Entropy increases during this process, as the milk and coffee blend. But yet this state is far more complex than the black coffee that proceeds it or the blended coffee that follows.

That complexity is the key to our puzzle.

The coffee is most complex while the coffee and milk blend.
Entropy increases as the coffee and milk blend. But the system is now much more complex than what came before or what follows.

This is where we live. This moment.

The coffee and milk blending, that’s our universe now. Rich in structure and complexity. As the universe continues to expand and stars give up their last light, we will return to a simpler state, with a vast void sparsely sprinkled with black holes, cool, burnt out stars, and their crumbs of dust and planets.

But we aren’t there yet. Galactic centers hum with star and planet formation, violent explosions mark the end of star life cycles and lead to new star formation. Small pockets like our planet Earth can decrease in entropy thanks to the useful energy we get from the sun. The sun’s increase in entropy pays the price: the entropy of the total universe still rises.

What is complexity?

Entropy we define according to the number of combinations the same state can have. If that number is high, entropy is high. Complexity on the other hand we describe as the amount of information required to describe something. The location, size, and shape of each milk plume in my coffee requires a much more lengthy description than either the black coffee I begin with or the blended coffee I end up with.

While putting together this blog post, I came across this video produced by Sean Carroll in collaboration with Minute Physics. They explain the concept much more succinctly than I have. Enjoy!

*If you take a 500 piece puzzle and pick pieces randomly, dropping them in the shape of the final puzzle, then there are 500! possible outcomes (that’s 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)! And only one of them is the correct configuration. If you include that the puzzle pieces may be oriented randomly, the odds vanish away.


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