Entropy

There is a concept that's crucial to chemistry and physics.

It explains why physical processes go one way, and not the other.

Why ice melts, why air leaks out of a puncture tyre, etc,.

It is entropy, which is responsible.

Entropy is often described as a measure of disorder.

This is convenient, but it could be misleading.

For example, which is more disordered?

A cup of crushed ice, or a glass of room temperature water.

We might think it is the ice, but actually the crushed ice has lower entropy.

Another way to think about entropy is through probability.

Let us consider two small solids, which are comprised of six atomic bonds each.

In this model the energy in each solid, is stored in the bonds.

They can be thought of as simple containers,

which can hold indivisible units of energy called quanta.

The more energy a solid has, the hotter it is.

There are many ways that the energy can be distributed in the two solids,

and still have the same total energy.

Each option is called a micro state.

For 6 quanta of energy in solid A,

and two in solid B, there are 9702 micro states.

There are other ways, the 8 quanta of energy can be arranged.

For example, all the energy in solid A, and non in solid B,

or half in A and half in B.

If we assume that each micro state is equally possible,

some of the combinations have a higher probability of occurring than the others.

That is due to their greater number of micro states.

Entropy is a measure of each energy configuration's probability.

The energy configuration, in which the energy is most spread out between the two solids,

has the most entropy.

In a general sense, entropy can be thought of as a measurement of this energy spread.

Low entropy means energy is concentrated.

High entropy means energy is distributed.

Entropy is useful for explaining spontaneous processes.

For example, a cup of hot coffee cooling down.

We need to look at a dynamic system where the energy moves.

In reality energy is not static.

It continuously moves between neighbouring bonds.

As the energy moves, the energy configuration changes.

Because of the distribution of the micro states,

there is a 21% chance, that the system will later be in the configuration,

in which the energy is maximally spread out.

There is a 13% chance, that it will return to starting point.

There is a 8% chance, that A will actually gain energy.

Because there are more ways to have dispersed energy and high entropy,

then concentrated energy, the energy tends to spread out.

That's why, if you put a hot object next to the cold one,

the cold one will warm up, and the hot one will cool down.

Even here there is a 8% chance, that the hot object will get hotter.

Why doesn't this happen in real life?

It is all about the size of the system.

Our hypothetical solids had only 6 bonds each.

We can scale the solids up to 6000 bonds, and 8000 units of energy.

We will start the system with 6000 quanta of energy in A,

and 2000 quanta in B.

Now we find that the probability of A spontaneously acquiring more energy,

is extremely tiny.

Every day objects have many many more times particles than this.

The probability of a hot object in the real world getting hotter is absurdly small.

It never happens.

Ice melts, and punctured tyres deflate,

because these states have more dispersed energy than the original.

There is no mysterious force pushing a system towards higher entropy.

Higher entropy simply has always a higher probability.

That is why entropy has been called time's arrow.

If energy has the opportunity to spread out, it will.