QUESTION #261

# The Second Law of Thermodynamics states that the universe tends toward high entropy. If so, what happens when there is nothing left to be disordered? How can matter be constant?

Let's start with the second question. Physicists would prefer to say that energy is conserved, not matter. In relativity theory we can convert one to another but energy is always conserved. That statement is not in conflict with the Second Law of Thermodynamics which states that in a closed system any process can either keep the entropy constant or increase the entropy of the system. The key is the form of the energy. In the universe today there are processes all around us that are converting one type of energy or another into heat energy. So the question is, what happens when all the usable energy is converted into heat?

That's a famous question that people thought a lot about in the nineteenth century. It goes under the name of the 'Heat Death of the Universe.' In short, once all of the energy in the universe is converted to heat then the universe will be in equilibrium -- everything will be of the same temperature and entropy will remain constant forever. This is complicated a bit by the fact that the universe is expanding. In an expanding universe you can never really reach equilibrium -- but the scientists of the 1800s didn't know about the expanding universe so let's just assume that the universe is static.

In such a universe we have a 'heat bath' of photons. These are the cosmic microwave background photons at a 'temperature' of 2.78 Kelvin. That's a pretty cold heat bath, and obviously you and I and the sun are much hotter. So we're not in equilibrium with the heat bath of the universe. But over time, as the sun burns hydrogen and as planets collide and break apart and as particles decay and so on, everything eventually ends up as photons or other elementary particles which eventually come to equilibrium. This is the conversion to 'heat.' The reason that we no longer worry about the heat death of the universe is that the time it would take for everything around us to convert to heat is many, many times longer than the current age of the universe. Our universe is marching very, very slowly towards equilibrium!
Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley

The second law of thermodynamics says that the total entropy of the universe can never decrease. Like other laws of thermodynamics this law is based on a statistical foundation and can be illustrated quite clearly by imagining that we can see the oxygen particles in a room.

Say that initially all of the oxygen molecules were grouped together in a nice regular pattern in one corner of the room. As time passes we can see that the molecules will begin to spread out. In a space as large as a room there is an almost infinite number of ways that the oxygen can arrange itself but only a very few of those correspond to states as organized as the one we began with. It is also reasonably easy to see why the state in which the molecules are randomly distributed around the room is the most probable. These two simple facts allow us to deduce that over time the molecules will spread out until they are randomly distributed. It is by calculating the number of possible states that the entropy is theoretically determined.

It is this pattern that makes physicists start to question the direction of time. In our room it is quite possible that for small periods of time the oxygen will begin to become more ordered but overall it will tend towards disorder. All of the laws of physics involved in the motion of the oxygen (Newton's mechanics and classical electromagnetism) are time reversible and so it should be equally possible for a randomly distributed set of molecules to accumulate in an order pattern like we began with. But it doesn't happen. This is because whichever way you point time it is more than likely that the particles will continue to spread out.

In the universe we observe a very definite direction in time. No-one is really sure why time flows the way it does but if it didn't flow intelligent life as we know it would not exist because of our reliance on the second law.

It is nearly universally accepted that the universe began in a much more compact and ordered state than it does now. If the Big Bang hypothesis is right then the universe began in a state of zero entropy. We can observe the matter in the universe spreading out and cooling down (i.e. cosmic microwave background) even now. If we apply the second law of thermodynamics to this then we can see that the universe will continue to spread out and become less ordered and if it survives for long enough will eventually end in the 'Heat Death' when all of the matter has reached equilibrium and the entropy is at its highest. There may well be almost infinitesimal fluctuations but other than that the universe as we know it will be dead.

On a final note it may seem that a black hole would violate the second law of thermodynamics because a singularity is the most ordered form of matter possible and should have an entropy of zero. However Stephen Hawking showed that the entropy of matter absorbed by a black hole is stored in the surface area of its event horizon and as such is released back into the universe as the black hole decays by Hawking radiation.

There are several equivalent statements of the Second Law that rather insightful:

1) During a process, if the system begins and ends at the same state, it is impossible that heat is completely turned into work.

2) Heat flows spontaneously from a hot object to a cold object.

3) The change in entropy is equal to the change in the heat along a reversible path divided by the temperature.

4) The entropy of an isolated system will always increase in a spontaneous process.

The last definition is essentially the one you are recalling.

The idea that entropy is disorder is not quite right and its unfortunate that this concept has been held onto so long.

Consider the case where a liquid freezes into an ordered crystal; according to the definition you give this should never happen but we know that it does -- Why?

A better definition of entropy would be the definition that is common to statistical mechanics and was proposed by Boltzmann.

Entropy can be thought of as being directly related to the number of ways a system has to `arrange' itself. Each arrangement constitutes a `microstate' of the system.

Therefore, a system seeks to maximize the number of different arrangements or microstates.

To make this clear think of a container full of a gas. The gas is occupying a constant volume and is also at constant temperature. Within the container the molecules of gas will explore different positions. If you could stop the system at some time you would find the molecules at some fixed positions. Collectively, their positions represent one possible microstate. Now start the system back up again and stop it some later time. Once again you will (probably) find the system in a different microstate. Given enough time the system will explore all possible microstates as well as ending up in the same ones. The more microsates the system has available the higher the entropy.

So you see entropy has little to do with disorder -- it's about microstates.

Entropy will always increase because a system is the most stable when it has the most microstates -- disorder is not the factor.

Matter isn't constant; energy is constant.

Consider the case when two atoms undergo a nuclear reaction and give off energy; something similar to a nuclear bomb or a reaction in a nuclear reactor. The mass (matter) of the products is LESS than what was started with -- mass has been lost! This is because the lost mass has been changed into energy.

The relationship between the mass lost and the energy produced is given by Einstein's equation:

E=mc2.

Energy -- not mass is conserved.
Answered by: Scott Bembenek, Ph.D., Theoretical Chemist