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?

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?

Asked by: Lisa

Answer

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.
Answered by: Edward Rayne, Undergraduate Physics Student, Cambridge, UK

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=mc^{2}.

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

'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'