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If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following.

The entropy of the universe always increases.

But does that include intermolecular forces, or interactions among particles in general?

For example, suppose we have a planet with an atmosphere. The planet does not rotate around itself. For some reason, at this moment, the atmosphere is uniform in density up to 10km away from surface. Clearly, soon, we will find that the density of air molecules near the surface increases and the density far from the surface decreases, and the density probably ends up following an exponential decay in relation to altitude.

In the above scenario, this natural process decreases the entropy of the universe due to the gravitational field of the planet.

So what about the 2nd law of thermodynamics?


EDIT: For clarity, the gas molecules on this planet are assumed to be chargeless spheres that only collide elastically.

For clarify again, the above example assumes that the entropy in statistical thermodynamics is indeed the entropy referenced in 2nd law.

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  • $\begingroup$ What makes you think the entropy of the universe has decreased in the process you described? $\endgroup$ – MonkeysUncle Apr 14 '15 at 5:32
  • $\begingroup$ There are typically two definitions for entropy. One that is taught most often is the logarithm of the number of configurations of a given physical state. If you let the air molecules "freely" choose their altitude, the uniform density is much more likely the exponential case. $\endgroup$ – Argyll Apr 14 '15 at 5:46
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For gravitational systems one has to be careful making statements about entropy and the second law of thermodynamics.

Your example is similar to the gravitational collapse of a gas cloud if you think carefully about it. In that case and in yours, the shrinking of the gas will raise it's heat. Now even though the increase of entropy due to the increased temperature isn't enough to save the second law, the emission of heat in the form of radiation is...

For more detailed discussion check out Please clarify how entropy increases when matter gravitationally coalesces and the link therein.

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  • $\begingroup$ Where does the emission of heat come from and how exactly does it save the second law? For my scenario, intermolecular forces are irrelevant. So we might as well assume they dont exist and it's probably ok to assume that all collisions are elastic too. So where does the radiation come from? $\endgroup$ – Argyll Apr 22 '15 at 11:29
  • $\begingroup$ (meant to edit this in) And what does it mean by "shrinking raises its heat"? $\endgroup$ – Argyll Apr 22 '15 at 11:39
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Widespread beliefs are not laws.

Look to the genesis of thermodynamics:
The short range interaction field, the electromagnetic one, that allows the atomic structure and the transfer of energy, heat, in the collisions of atoms and molecules was, for sure, present in the analysis of the thermodynamics since its inception. In this original context the validity of the laws is unbreakable (except for brief moments).

The long range interaction field, the gravitational one, was absent from the analysis since ever. Without a proper study of this situation no one should take for granted that the laws should apply. Unfortunately there is a widespread belief that the universe must obey to our convictions.

Lets see this simple situation with matter and gravity:
An infinite universe, isotropic and isodense except in two locations. The initial temperature is Zero (0 K).
(In the past I'd insurmountable intellectual problems that ended once I was able to concede that the whole universe can not be ascribed to the size of an atom, or of a tennis ball or inside my head)
Consider a underdense region: ...----------__----------...
You can imagine the universe as a previously immobile lattice of crystal with an atom at each seat. But the atoms that are missing in that region are the ones that, if present, were holding the all universe immobile in place. No more the atoms in the vicinity of that hole will be attracted to that region and the hole starts to grow. A hole will develop bigger and bigger concentrating all the matter in the outer shell of it. The growth of the hole is accelerated (The relevant gravitational equations are originally presented here and here) and the temperature will rise - once again: against the general belief.

The resultant of the growth of the primordial holes are the largest structures of the universe: the VOIDS.

But, by BBT, everybody knows that the universe was hot in the beginning. This is theory - a belief - and the data (voids) allow the opposite interpretation.

An overdense region: ...______/\_______... is condemned to disappear and dissolve in the immense ocean of surrounding matter (once again: against the general belief: gravitational condensation)

It is the immense ocean of surrounding matter that dictates the evolution of the local particulars. IMO the opposite notion is irrational.

The codes of the simulations of the universe evolution are flawed and they can not achieve the gigantic proportions of the voids, as well as their degree of emptiness: They are considering an infinite speed of light; they are not accounting correctly the infinite character of the universe; they are not starting with 0K, they are manipulating the data by injecting theoretical 'dark matter' and 'dark energy'.

note: DM and DE are not observational evidence, they are injected in the theory and in the simulations to fulfill the tremendous misalignment (95%) between the accepted model and the observed data.

Everything I wrote above is also a belief, backed with the equations of the usual gravitational interaction and argumentation on physics. The documents linked in my profile are formal presentations 'against the tide'. Instead of space expansion I explore a 'shrinking atom' and found a model 100% aligned with the data (no DM, no DE, no...) and with 1 parameter: $H_0$.

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    $\begingroup$ the first two paragraph are fine but I am not sure what the rest is about.... $\endgroup$ – gatsu Apr 14 '15 at 9:13
  • $\begingroup$ @gatsu: it is about gravitational physics in a large universe starting at 0K (not seen elsewhere). I've done my best to ease the presentation to all. I'd appreciate to know what is not clear or to see your own answer or objections. $\endgroup$ – Helder Velez Apr 14 '15 at 9:29
  • $\begingroup$ for starters, I don't consider "a large universe at 0K" a simple example, especially when no equation or back of the enveloppe calculation follows. $\endgroup$ – gatsu Apr 14 '15 at 9:37
  • $\begingroup$ The question is about the general validity of thermodynamic laws under gravity and there is no need to justify any cosmological model as long as a finite gravitational speed of the interaction exists (I should have mention it). @gatsu: see the notion in this PSE-Q I showed that a large enough or infinite universe will not collapse under gravity (against..). I'd love to see arguments instead of vagueness. $\endgroup$ – Helder Velez Apr 14 '15 at 10:14
  • $\begingroup$ First of all, I am actually asking about second law under attractive interactions in general, not only gravity. Gravity merely makes a convenient example. Then.. how does evolution of universe relate to my question about entropy? Are you suggesting that second law is false? At no point in your example is the word "second law" or "entropy even mentioned. $\endgroup$ – Argyll Apr 22 '15 at 11:37
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You state the second law as :

The entropy of the universe always increases.

In my college textbook it is stated as :

Processes in which the entropy of an isolated system would decrease do not occur, or, in every process taking place in an isolated system, the entropy of the system either increases or remains constant.( F.W.Sears an introduction to thermodynamics, the kinetic theory of gases and statistical mechanics, second edition 1959, page 111)

bold mine.

But does that include intermolecular forces, or interactions among particles in general?

It includes everything once the underlying framework is revealed, that of statistical mechanics. In this entropy is defined as: S=k*ln(W) where W is the thermodynamic probability (p 281 in above reference). Classical thermodynamics is an emergent framework from statistical mechanics and finally quantum statistical mechanics.

the gas molecules on this planet are assumed to be chargeless spheres that only collide elastically.

This site discusses physics as is known on Earth and documented with data and models that fit the data. There are no chargeless spheres in our universe, and this was known even at the time that quantum mechanics and particle physics were yet to be revealed. Thermodynamics and its predictions using classical mechanics and classical electrodynamics was the underlying level on which quantum theory emerged. Classical thermodynamics tried to accommodate black body radiation and could not, so quantization of radiation had to be assumed. Radiation is part of all the physical systems, all bodies emit black body radiation.

Thus an isolated system counting thermodynamic probabilities statistically has to include black body radiation. This radiation is the result of the scattering of neutral ( not chargeless) bodies on neutral bodies, distorting the charge distributions and turning part of the energy into electromagnetic radiation ( even classically).

So your billiard balls settling on the earth will lose kinetic energy and this loss is ultimately into electromagnetic radiation ( possibly some gravitational radiation too but it is so weak with respect to electromagnetic that one can forget it). To calculate the entropy you have to catch all those photons and count the microstates that are created by their existence.

Thus Ali's answer is correct.

Your example is not different from dipping a crystal seed into a solution and getting a highly ordered crystal. The entropy of the crystal is low, but in the process the liquid and all the radiation related to the process should be counted in. The same is true with all living matter, where life is a battle of decreasing entropy within the live body while it increases exponentially with all the chemical processes and electromagnetic radiations going on through life.

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  • $\begingroup$ Is there an easy way to see that the black body radiations would indeed increase the overall entropy? $\endgroup$ – Argyll Apr 22 '15 at 13:21
  • $\begingroup$ As well, I am perfectly aware of the statement of 2nd law you referenced. What I wrote includes the word "imply". What I am truly looking for, is a detailed explanation that goes beyond merely pointing out why 2nd law might hold or a simple rejection that 2nd law is "not laws" (as suggested in another answer). I don't think I can understand why 2nd law IS in effect other than it might from your answer yet. $\endgroup$ – Argyll Apr 22 '15 at 13:24
  • $\begingroup$ In the framework of statistical mechanics the second law is not a "law", it is derivative from the statistics. In the framework of thermodynamics it is a law. Each framework has its elegant mathematical formulation around the postulates . In thermodynamics it is a law, similar to calling axioms axioms in mathematics: necessary for the developement of the theory. It is a bonus that we discovered that thermodynamics is emergent from statistical mechanics, and can explore why at the gross thermodynamic frame we call it a law : because of the tiny probabilities involved in destroying it. $\endgroup$ – anna v Apr 22 '15 at 13:59
  • $\begingroup$ Suppose you have two molecules in a box. They can be described by N transpositions. When they collide, they are no longer two, a photon is released by the collision and that increases the number of possible microstates factorially (whence the photon came, where were the molecules, etc). A photon is a particle, and black body radiation releases zillions of photons, and extra collisions even more. $\endgroup$ – anna v Apr 22 '15 at 14:01

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