# If thermodynamics says entropy always increases, how can the universe end in heat death?

My understanding of entropy is that it is a measure of the available states a system can take on. In this context, if the total entropy in the universe always increases, how can it lead to a configuration where everything is at absolute zero? This has an entropy of 0, as there is only 1 possible configuration of the universe where this is the case.

• The idea of heat death doesn't necessarily mean absolute zero. – JMac Nov 29 '19 at 19:28
• it increase to a certain limit, the one at thermal equilibrium – Wolphram jonny Nov 30 '19 at 0:59
• Is this a macrostates / microstates confusion? – usul Nov 30 '19 at 15:35
• Define universe. Observable universe? – Peter - Reinstate Monica Dec 2 '19 at 0:12
• What difference does the distinguishing to 2 make? From the answers below it seems that for both cases it is an open system which doesn't subscribe to the second law of thermodynamics, which only applies to isolated systems? – Vishal Jain Dec 2 '19 at 12:03

the total entropy in the universe always increases

The total entropy of any isolated system increases until equilibrium is obtained. Then entropy stops increasing. If the system is the entire universe, then entropy will increase until the heat death.

how can it lead to a configuration where everything is at absolute zero.

The universe being at maximum entropy does not mean the entire universe is at absolute zero.

This has an entropy of 0, as there is only 1 possible configuration of the universe where this is the case.

Not at all. Maximum entropy means there are a maximal number of configurations.

As a useful analogy, just think of the gas in a box example. The box has a "heat death" when maximum entropy is obtained when there is a uniform gas concentration throughout the box. This doesn't put the box at absolute zero, and it doesn't put the box in a state that only is associated with a single configuration.

• Well yes, but in an expanding universe, the equilibrium state is at 0K. (According to current models, to the best of my non-expert understanding.) It basically means that all matter-energy is in the form of photons with infinite wavelength. This is an asymptotic state of course, not one that will actually be reached. – Nathaniel Nov 30 '19 at 11:54
• @Nathaniel The asymptotic limit is also an infinitely large universe, which you’re not taking into account. – Mike Scott Nov 30 '19 at 12:40
• @MikeScott am I not? Why do you say so? – Nathaniel Nov 30 '19 at 13:46
• @Nathaniel You may very approximately take the total entropy of the universe to be temperature * volume. You’re asserting that this tends to zero as the temperature tends to zero, which it would do for a finite volume, but doesn’t do for a volume tending to infinity. – Mike Scott Nov 30 '19 at 14:31
• @MikeScott I didn't say anything remotely resembling that. I only said the temperature will tend to 0. I didn't say anything about the total entropy, which obviously would be very large, not zero. – Nathaniel Dec 1 '19 at 16:06

You may be confusing "heat death" with "energy death". Absolute zero can imply energy death as temperature is a measure of kinetic energy. But heat is energy transfer due to temperature difference. Which is another way of saying heat is energy transfer due to thermal disequilibrium. Natural processes, ones that increase entropy, decrease thermal disequilibrium. In theory at some point temperature differences in the universe will cease at which point heat transfer is no longer possible. Thus the term "heat death". But the elimination of temperature differences is not the same thing as saying the temperature of everything in the universe will eventually be absolute zero. Just that they will be the same, whatever that temperature is.

Temperature differences are not the only form of disequilibrium. There is also the disequilibrium associated with forces (including gravity) or pressures. These are forms of mechanical disequilibrium. Natural processes that increase entropy result in mechanical equilibrium. If all forms of mechanical disequilibrium are eliminated, there is no longer the possibility of processes that produce mechanical work, the other form of energy transfer.

As Wikipedia puts it, the "heat death" means the universe will "evolve to a state of no thermodynamic free energy and would therefore be unable to sustain processes that increase entropy". Entropy is maximized.

Hope this helps.

Entropy of a closed system doesn't increase without a limit. It increases until thermal equilibrium.

It is not a zero absolute temperature point. It is the point where the whole system has the same temperature.

However, currently the Universe doesn't look to be a closed system.

Due to the expansion of the Universe, we are actually more far and far away from the heath death with time. The Universe is lesser equilibric as it was some billions of years ago. For example, the $$\approx$$ 300000 year old Universe, in the era of the initial (re)combination, was a nearly static, level distributed gas.

In this sense, we could say, the heath death won't happen, it already happened.

• This is a good point. The entropy content of the universe is already extremely close to the maximum value it will ever attain. – Eric Lippert Nov 30 '19 at 19:10
• If the universe is an open system, how can we say there is any equilibrium condition for it? Where did this notion of heat death come from then, if not as the result of the universe coming to equilibrium. – Vishal Jain Dec 1 '19 at 15:24
• @VishalJain The expansion of the Universe is a new development, for example Einstein created SR and GR originally for a static, not expanding Universe. The expansion became known no early than the 30s. The concept of the entropy became known around in the second half of the XIX. century. Between these, the heath death concepts had a big banzai. Since then, Big Bang, Big Rip and so are the major eskatological concepts of the Astronomy. – peterh - Reinstate Monica Dec 1 '19 at 16:15
• Currently the universe may well be infinite which is rather the antithesis to "closed system". Not the part we can observe though, which becomes emptier and emptier. – Peter - Reinstate Monica Dec 2 '19 at 0:17
• @Peter-ReinstateMonica I asked my astrophysics professor about this he said that the universe does not expand into something and so you can think of it as a closed system since it is self contained, thus the second law of thermodynamics holds and you will have heat death. – Vishal Jain Dec 2 '19 at 14:26

If the universe is expanding infinitely, and all configurations are achieved (as in the above mentioned 'asymptotic state'), then this ceases to be an 'isolated system'. The second law of thermodynamics applies specifically to isolated systems (which are not actually so easy to come by at large scale).

• So it is incorrect to apply the second law of thermodynamics to the universe? This has been done by pretty much every thermodynamics lecturer Ive watched. – Vishal Jain Dec 1 '19 at 15:25