[Lewis Thomson (OP)]

Donald has presented this question to the Naked Scientists

"Entropy is ALWAYS increasing. There must be a metric that scientists use to measure entropy. It follows that the lowest entropy state was at the big bang. What is the shape of the entropy curve of the universe, and where are we compared to the maximum amount of entropy possible?"

What do you think? Discuss in the comments below...

[evan_au]

There must be a metric that scientists use to measure entropy.

There are multiple measures of entropy, depending on what you are measuring, but they are related to each other.
- It was originally developed in the context of optimizing steam engine output
- It was later applied to understanding the behaviours of large numbers of molecules
- Even later it was applied to information
- And now it has been applied to biology and economics (with various degrees of success)

https://en.wikipedia.org/wiki/Entropy#Approaches_to_understanding_entropy

Entropy is ALWAYS increasing.

That is true on the scale of the whole universe.

But it is not necessarily true - you can reduce entropy locally by expending energy (which produces a greater increase in entropy elsewhere). The overall entropy increases.

[chiralSPO]

The short answer is "yes, we can measure entropy"

The long answer includes many definitions and caveats.

From a statistical mechanics perspective, entropy is proportional to the log of the number of equivalent microstates possible:

S = k×log(w)

So, what does that mean?

Imagine we have an 8×8 grid with 8 checkers that can be placed on it.

We can describe a state, A, in which all checkers are on the bottom row. How many equivalent microstates does this include? Well there are 8! ways of placing 8 checkers in those 8 squares (8! = 8×7×6×5×4×3×2×1 = 40320); ie there are 8 possible squares for the first checker to be in, then once that is selected, there are 7 squares that the next one could occupy, and so on until all 8 are filled.

We can describe another state, B, which is defined as none of the 8 checkers is touching the edge. This means there are 8 checkers being placed in a 6×6 grid. So there are 36×35×34×33×32×31×30×29 (≈ 1.2×10¹²) ways of arranging those checkers such that they could be described as being in state B.

If we were randomly moving the 8 checkers around, they would be much more likely to be in state B than state A.

This can be extended to thinking about other, more complex systems, but the basic idea is exactly the same.



We can also think about entropy thermodynamically. The change in entropy of a changing system is the derivative of the change of free energy of that changing system with respect to temperature:

ΔS = d(ΔG)/dT

This is much harder to think about, but much easier to measure in the actual real world!

As far as the shape of the entropy curve of the universe: on a large scale, it is probably best thought of as roughly a sigmoidal curve (exponentially increasing when moving from highly ordered to less ordered), but then asymptotically approaching "maximal" entropy. Because of the statistical nature of things, it is *possible* for the entropy to decrease at any point, but it is highly unlikely to, unless the entropy is already maxed out, and then it may decrease slightly, but then will be at a point where it is equally likely to increase as decrease, and will essentially remain unchanged. So there might be little wiggles in that asymptote. If you go out to infinitely distant in times, it is theoretically possible (or even necessary, depending on assumptions) for those wiggles to go back down as far as the starting point, but we are talking about limits approaching infinity, so...

In any case, the universe is VERY ordered (very low entropy) compared to what it will be later.