# Can entropy of Universe be constant?

If I understand entropy correctly, then for example two objects orbiting a centre of mass have lower entropy than when said objects eventually crash into each other and form a new one.

So let's say that a typical galaxy spirals around its centre of mass and eventually objects within it will fall into the center thus increasing its entropy.

But if the entropy of the Universe was somehow to be constant, then maybe that's why space is expanding? As each galaxy becomes more chaotic while objects are going closer and closer together these galaxies are at the same time becoming more and more spread apart thanks to expansion of space.

I don't know the exact calculations of entropy, but is it possible that there is a mechanism triggering space expansion as a reaction to gravity increasing local entropy?

Also gravity is increasing in intesity when the distance between objects is shorter, so the longer two masses are gravitating, the shorter the distance between them and then the more intensive gravity becomes over time. This might correspond then to the increasing speed of expansion of Universe, as it has to compensate faster to keep entropy constant.

Forgive me if what I said above is completely incorrect; I've been thinking about entropy and came with this idea, but I'm no professional physicist and would like to know if any of the above make sense.

• – Kyle Kanos Apr 2 '14 at 16:37
• You have to explain first what you mean by "entropy of the Universe". Stars are often considered as Newtonian gravitational system of particles and thermodynamic (Clausius) entropy does not apply to such systems. – Ján Lalinský Apr 2 '14 at 17:31
• the effect on structure formation within an expanding universe on its expansion is discussed by cosmologists as 'Backreaction of inhomogeneities on the expansion' – chris Apr 9 '14 at 8:29

Yes and No

Yes part

If you think of the whole Universe as a closed system, then the entropy must be constant. According to quantum mechanics, the evolution of a closed system is unitary. The unitarity forces us to believe that the whole universe can be thought of as a reversible computer and so a big fine quantum computer. Now since the whole process is reversible, entropy change should be zero. It means that the total entropy of the universe can be constant.

No part

If you think of the Universe as an open system, then non-unitarity comes in place. Furthermore, irreversibility pops out as a result which powers entropy change, so entropy need not be constant.

Since we don't know the over all topology of the universe , we can't say anything about the universal thermodynamics. Anyways , Quantum thermodynamics at the global level would be the keypoint in both cases.

• What role is unitarity playing here? I don't think it's correct to say the entropy of the universe is constant. If you want to consider it as a closed system you could compare it to the microcanonical ensemble, but this system (the universe) is still evolving towards equilibrium (towards the state of maximum entropy). So I don't see any reason to say it is in thermodynamic equilibrium, but I don't know much cosmology so I can't comment further. – Julien Apr 9 '14 at 7:42
• @Julien The quantum evolution of a closed system is unitary (One of the postulates of Quantum Mechanics).Now your very statement "system (the universe) is still evolving towards equilibrium (towards the state of maximum entropy)" seems incorrect as it may be possible that universe as a whole is at eqb and what you call "evolving " is nothing but the transition of this microcanonical ensemble from one accessible microstate to another (which we can't ignore in a watertight argument. If Universe is not a closed system , then what follows(2nd para of my answer) need not hold. – Kishor Bharti Apr 9 '14 at 8:06
• I have edited my answer to include the case of Universe as an open system. – Kishor Bharti Apr 9 '14 at 8:16
• @KishorBharti I liked your answer the most, I think some people misunderstood my question and were thinking about entropy in far future (i.e. heat death of Universe) while I was asking about possibility of constant entropy throughout the entire existence of Universe. This theory about Universe being quantum computer is really interesting, do you maybe have some more articles about that? I would like to read more about this theory. – Ardath Apr 11 '14 at 8:16
• Thanks for your remark.I would look for some. I would need your mail-id for the same. – Kishor Bharti Apr 11 '14 at 13:20

As far as I know, the expansion of the universe contributes into creating more and more microstates. This is almost equivalent to saying that entropy increases (because $S = k_B$ln$(\Omega)$). We cannot be sure that the law of entropy applies to the whole universe (There is debate if the universe is a closed system or not, if its infinite or finite, etc..) but from what we know the disorder of the universe is increasing due to this large number of microstates increasing with time, leading to the disorder of the universe increasing.

Entropy is a natural tendency of the Universe to fall apart into disorder.

In a reversible process, an increase in the Entropy of the system will be exactly equal to the Entropy decrease of the surroundings. Thus, the net change in the Entropy of the system and its surrounding will be zero.

But in an irreversible process in an isolated system (for example, all thermodynamic processes) the entropy is always increasing. This stems from the Second Law of Thermodynamics.

Whenever there is a decrease or release of energy, the Entropy increases. This means that Entropy is also a measurement of how much usable energy there is. The Entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium, the maximum Entropy. Change in Entropy is defined as $$\Delta S=\int \frac{dQ}{T}$$ where $T$ is the uniform thermodynamic temperature of the system and $dQ$ is the incremental reversible transfer of heat into that system.

The Sun, and every other star, is radiating heat into the universe. But they can’t do it forever. Eventually the heat will have spread out so much that there won’t be warmer objects and cooler objects. Everything will be the same temperature. As all of this happens, the Entropy of the Universe keeps increasing. Thus, it was speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source. The expansion you are talking about leads to the Universe getting colder faster.

When this heat death is reached, the Universe will attain a thermodynamic equilibrium and will have maximum entropy (which will essentially be constant).

• Then the question could be: "Is energy in Universe conserved?" Lately I red a lot about how expansion of space contradicts conservation of energy. So IF energy weren't conserved then naturally there would be a way to lower entropy and hence my question about it being constant instead of energy. – Ardath Apr 6 '14 at 20:31
• @Ardath Yes I've also read about the expansion contradicting the conservation of energy, and it is most likely true. We know that dark energy is increasing as the expansion is accelerating, and it is not possible for dark energy to be conserved in any way that we know of. – user42733 Apr 6 '14 at 20:51
• You might want to slightly change the first sentence. Entropy is the log of a number of states, it is not a tendency? – chris Apr 9 '14 at 8:21
• @chris- How is it now? – user42733 Apr 9 '14 at 10:57
• Sorry I meant, how is it not? – user42733 Apr 9 '14 at 20:31

It is common to hear in cosmology that the entropy of the universe is adiabatic (constant) at late times. In the standard model of cosmology, $\Lambda CDM$, the universe is dominated at late times by the cosmological constant that causes exponential expansion of the universe. During this epoch, the formation of new structure is limited by exponential decay, so we can say at late times, structure cannot form. This is often taken to mean that there is effectively no interactions between matter-matter, radiation-radiation, or matter-radiation. Since the entropy of the universe can't decrease and since it would require some kind of interactions to increase the entropy, cosmologists thus often say that entropy is constant at late times.

Now, whether or not this is actually the case is uncertain (that is, I don't really know for sure), but even if it is not exactly constant, we can say the entropy of the universe would not change by a significant amount in late times once the cosmological constant dominates the energy density of the universe.

Yes it can be, if the Universe attains equilibrium.

• Can you explain how equilibrium allows this, or otherwise elaborate a bit more? – Kyle Oman Apr 2 '14 at 18:30