# Why don't the first two laws of thermodynamics contradict each other?

The second law of thermodynamics states that the entropy of the universe increases over time and this has lead to theories like the heat death of the universe and the big rip. What this means in effect is that all matter and energy has an expiration date, beyond which it gets divided accross infinite space and this is irreversable since entropy does not move backwards.

The first law of thermodynamics states that energy cannot be created or destroyed. The only explanation this leaves for the universe's existence is that energy has existed since always and never had to be created.

And herein lies the contradiction: If energy has been around for an infinite amount of time, why hasn't the heat death or the big rip already taken place? How come we are able to observe the universe in its current fairly organized transitional state unless A. energy was created a finite amount of time ago or B. Energy has existed since always but it can freeze or move backwards entropy-wise allowing us to observe it in its current form. Either way one of the two laws is violated.

How do physicists reconcile this paradox?

• You probably heard of the so called big bang, where the universe started some time ago? so we dont' know anything before that. Commented Jul 12, 2023 at 10:00
• One needs to understand what "laws" ( principles, postulates, ...) are in the mathematical models we use in physics. They are extra axioms applied to the particular mathematical model, thermodynamics in your question. see also my answer here physics.stackexchange.com/questions/259076/… . thermodynamics cannot hold at the beginning of the universe . Commented Jul 12, 2023 at 10:52
• Commented Jul 12, 2023 at 11:19
• It's not energy that is important. It is an energy gradient that is important. At some distant future time, all energy will be uniformly distributed throughout the universe, no energy gradients will exist, and no work and no life can exist as a result. Commented Jul 12, 2023 at 18:14
• @Dimitris02 for something to be called energy creation, there should be a time where energy didn't exist, then at a later time, the energy existed. What if t=0 is the beginning of time and energy just existed there? then there is no energy creation. my point is similar to other answers, we don't know much about the beginning, and the laws certainly isn't to prescribe things beyond our observations, it's just to describe what we can observe. Commented Jul 13, 2023 at 4:21

What I'm saying is that the big bang had to be either a case of energy creation or entropy reversing. Therefore one of the two laws is demonstrably false

Our physical laws describe the universe around us. We observe energy conservation and entropy increase, and we have developed experimentally verifiable laws around these principles.

You're trying to apply these laws beyond our observations. We don't know anything about what was before the beginning; we can't apply our laws there. Our laws are true for the universe we have now though.

• In other worlds: the big bang is a singularity of the current theories of physics, a point in spacetime that falls outside of the domain of these; and we do not have a higher level theory whose domain does include this point (i.e. resolves the singularity). Commented Jul 13, 2023 at 8:35
• @Neinstein: More generally, many physical laws are approximations which do a good job of describing reality in some cases, but deviate substantially from reality in others, and it's entirely possible that laws which are thought to hold in all cases only do so because deviations in observed cases are too small to measure. Measurement of the relationship between the temperature and pressure of a gas which are taken at 500K and 700K don't imply anything meaningful about how it will behave at 273.2K. Commented Jul 13, 2023 at 22:36
• @supercat True, but that's actually a different case. What you describe is a region where the theory does not work anymore. It still gives predictions, though inaccurate ones, because we neglect an "undiscovered" effect. But a singularity is more than that. It's a point (or region) in spacetime where the differential equations of the theory are outright invalid, like when a division by zero or a discontinuity happens. That means we can't even make inaccurate predictions, i.e. we have totally zero clue wtf is happening there. Commented Jul 14, 2023 at 7:31
• @Neinstein: Would it actually be a division by zero, or a division by a number which would probably (because of undiscovered effects) be non-zero? Commented Jul 14, 2023 at 14:41
• @supercat It is a division by zero in the current model. To account for the new effects, you need a new model, because the current one is simply invalid at that point, not just inaccurate. Commented Jul 17, 2023 at 6:55

The main thing to say is that physics deals in laws that describe but do not necessarily prescribe. That is, they mostly succeed in expressing, in a useful and concise way, things that are observed to hold in the universe; they give a description of what is observed. They do not themselves act like some sort of police force making sure the law is upheld or anything like that.

What this means is that physical stuff might not always have had the patterns it is observed to have now, and it might not always continue to have those patterns. So any law might be partial, only applying to some part or some period. But of course we are interested in the widest longest patterns, and energy and entropy are certainly among those. It is just that we can't reasonably claim much in the way of confidence that those patterns have held for an eternity. Who knows? Maybe something else happened in the past. Observations related to Big Bang and very early universe suggest that something different may have been happening, as regards energy and entropy, at some very early period.

If you have a pyramid made of spheres, like cannonballs: the First Law says that the total number of cannonballs will never change. The Second Law says that over time the pyramid structure will fall apart until all the balls are at the same level on the ground, and will never spontaneously stack themselves.

• Presumably there is a vanishingly small but finite probability of the balls re-stacking themselves. If time goes on for ever, then this event will happen eventually. Commented Jul 13, 2023 at 8:35
• @chasly-supportsMonica But the universe is also expanding, so there will be more room for them to be spread out, making reassembly less likely. Commented Jul 13, 2023 at 13:28
• This is sort of a bad metaphor because the cannonballs fall apart because that is the lowest energy configuration, not because the pyramid structure is a highly ordered configuration per se. A better example might be a frictionless game of pool. If all the balls are the same color, shortly after breaking it will be hard to tell which ball you hit and which balls were hit. They will all be moving around randomly, but the kinetic energy will be the same (ignoring the Poincare recurrence theorem). Commented Jul 13, 2023 at 18:07
• I would argue that thermodynamic systems evolve due to an entropy gradient in many cases, just as the pyramid falls due to a gravitational gradient. Commented Jul 14, 2023 at 2:43
• @chasly-supportsMonica +1. Given infinite time, an apple in a magic box will turn back into an apple. The Most Misunderstood Concept in Physics Commented Jul 15, 2023 at 1:17

When books and professors discuss the "thermodynamic universe" the word "universe" is not meant in a cosmological and eschatological sense, They are talking about a piece of matter $$\mathcal M$$, the "system", that is subjected to boundary conditions. These boundary conditions are represented by prescribed fixed values of certain energetic potentials, such as, temperature, gravitational potential, electrochemical potential, etc.. The sources of these potentials are visualized as reservoirs whose size is, ideally, infinitely large, in practice, so large when compared to $$\mathcal M$$ that in all processes of interest the relative change in any of the reservoirs is negligible to that of occurring in $$\mathcal M$$. The thermodynamic universe that is analyzed in thermodynamics, in this sense, is all these reservoirs AND $$\mathcal M$$.

Understood this restricted way for which we have direct experimental evidence, for such universes, note the plural, the entropy always increases and the question when will we reach heat death or some such makes no sense.

• Along these lines, but with respect to the OP's more idiomatic use of the term "universe" as well as his use of the "cosmology" tag, there are definitely cosmological models, like the "Janus Point" model posited by the mathematician Julian Barbour, that rely upon gravity (rather than thermodynamics), in explanations for the apparition of reality. Commented Jul 12, 2023 at 17:51

Physicists reconcile this paradox by insisting

1. The universe has only been around a finite amount of time

2. The universe was originally in a very low entropy state

You are free dispute either claim, but on this topic there is the famous quote from Arthur Eddington:

The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation.

Edit: it seems the real paradox the OP wants to resolve is how something could come from nothing. On this point physicists have a convenient out. Our least controversial theory of the origin of the universe predicts that there is not a good time coordinate near the start of the universe, which gets us out of trouble in two ways

1. We don't have to worry about what happened "before" because there is no "before" to worry about.

2. Energy conservation and time invariance are two sides of the same coin per Noether's theorem. If there is no well-defined time, then we shouldn't be upset if energy conservation breaks down.

I think one aspect that has not been pointed out yet, is that on a quantum scale energy conservation and monotonous increase in entropy are not always given, due to the uncertainty principle. On a quantum scale energy can spring into existance or be destroyed or entropy can decrease, only in the long run (or on larger scales) will the laws of thermodynamics hold.

In quantum mechanics this leads to a phenomenon called quantum fluctuation, which says that no quantum field is ever completely flat, but even in a low energy state there are always tiny energy fluctuations or matter/anti-matter particle pairs going in and out of existance.

Right after the big bang cosmic inflation happened. In an extremely short period of time the universe massively increased in size. The result of this is that due to the quantum fluctations the universe after cosmic inflation was not generally flat but had a matter and energy distribution that resembled the irregularities of the quantum fields but on a much larger scale. These irregularities in matter and energy density then became the seeds for the galaxies of today.

In conclusion, the laws of thermodynamics don't hold on quantum scales and the big bang has scaled up the quantum effects to a galactic scale, so this is where the low entropy state in the beginning comes.

I'm not a physicist and this explanation is probably incomplete, but I think the quantum violations of thermodynamics and cosmic inflation need to be mentioned here.

• How do physicists reconcile this paradox? Ditch relativity, +1. Commented Jul 15, 2023 at 1:19

What I'm saying is that the big bang had to be either a case of energy creation or entropy reversing. Therefore one of the two laws is demonstrably false

The other answers have done a good job of answering the question - I'll just add that it is possible to apparently reduce entropy in a local area while increasing entropy somewhere else. Think of an air conditioner - it appears that entropy is being reduced between the inside and outside of your house, but entropy is being increased (more) at the power plant. Since we don't know what happened before the Big Bang (in my analogy, where the power plant is), it's entirely possible that what you see as "entropy reversing" might just be air conditioning.

It's not necessarily just that we "don't know anything about what was before the beginning" of the universe: That may be the case, but it may also be the case that the universe has always existed.

As place names in English are capitalized, the OP (who used "the universe" rather than "the Universe") was referring to "the universe" in the sense of "everything", rather than "the Universe" in the sense of a locality causally separated (i.e., "out of contact with") any and all other causally-separated localities.

In the extremely broad context of "everything", the most well-known cosmological model for a universe that has always existed is Sir Roger Penrose's "Conformal Cyclic Cosmology", detailed in a 2010 book titled "Cycles in Time", by Penrose (a mathematician and frequent collaborator with the late physicist Stephen Hawking), who has been knighted by the British government, as well as awarded by the Nobel Prize Committee, for other contributions to physics.

• As a Creator without employment does not provide a very good role model for His or Her brightest creations, the conclusions reached by Penrose might not have been publicized in periods much earlier than our own. Commented Jul 12, 2023 at 16:51

Besides the applicability of Physical "laws" well explained by @BioPhysicist, there is fact that Thermodynamic is entirely a STATISTICAL science.

There is NO hard limit. Entropy reversing is NOT "impossible", just very, very, very, very, (one "very" for each atom in the Universe)... unlikely.

Yes, there is a contradiction among between the 1st & second laws of thermo and your conception of time. What it means is that these laws, or the notion of time are imperfect, require revision, and cannot be reliably used for extrapolation to conditions beyond that where their supporting evidence was collected. This happens all the time; Newton developed a fine set of laws of motion, however extrapolating these to relativistic velocities simply didn't work. A new, improved theory is needed.