# Explaining atoms and bonding using entropy

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micklat
TL;DR Summary
In origin of life science, the "why" is answered by entropy. Life speeds up the movement to maximum entropy. How far can we go back? Can we explain atoms and atomic bonding as an emergent phenomenon that allows the universe to move towards max entropy?
I am a biology undergraduate interested in abiogenesis.

The entropic explanation for the origin of life is that life is allowed to exist because it increases universal entropy.

I am curious about how far we can take this theory down.

How can you explain the emergence of atoms and atomic bonding as processes that contribute to universal maximum entropy?

Staff Emeritus
How can you explain the emergence of atoms and atomic bonding as processes that contribute to universal maximum entropy?

I don't think you can. Entropy is something that emerges when describing many-body systems. The hydrogen atom, for example, only has two.

Demystifier
Mentor
The entropic explanation for the origin of life is that life is allowed to exist because it increases universal entropy.

Do you have a reference for this statement? I have never seen such a thing advanced as an "explanation" for the origin of life. Lots of things that, if they happened, would increase entropy, nevertheless fail to happen. So just saying that something increases entropy does not explain why that thing happened.

micklat
Do you have a reference for this statement? I have never seen such a thing advanced as an "explanation" for the origin of life. Lots of things that, if they happened, would increase entropy, nevertheless fail to happen. So just saying that something increases entropy does not explain why that thing happened.

thankyou explanation is the wrong word. More http://www.englandlab.com/uploads/7/8/0/3/7803054/2013jcpsrep.pdf and for a less detailed https://aeon.co/essays/why-life-is-not-a-thing-but-a-restless-manner-of-being

Mentor
explanation is the wrong word

Indeed. But that leaves me confused as to what your actual question is. If you're not looking for an "explanation", what are you looking for?

Life has more structure (= less entropy*) than a corresponding soup of particles, a collection of bound systems like atoms also has more structure (=less entropy*) than a corresponding collection of unbound systems. Is the process of formation of these structures similar from the point of view of thermodynamics?

For the primordial processes, the answer is no. Abiogenesis (the formation of life) has happened under very special conditions far from thermodynamic equilibrium while the primordial formation of atoms is a cooling effect due to the expansion of the universe.

Also the reasons why a living system and bit of ordinary matter which is somehow structured (like hydrogen gas contained in a box at room temperature) don't transition to a less structured state are very different: life is sustained by exchanging matter with its environment while in the case of the hydrogen gas, there simply isn't enough energy to reach a state where the molecules are split into individual atoms (and even less so for splitting the atomic or nuclear bonds). Speaking physically, the second law of thermodynamics requires that life dumps entropy to its surroundings while for the hydrogen gas, the first law of thermodynamics forbids the transition. Entropy becomes only relevant if the process in question is possible energetically.

Having said this, there are similarities. Let's say we have a collection of particles which can be either in free states or in two-particle bound states of lower energy. So in order for a bound state to be formed, there is excess energy which needs to be carried away somehow. In many everyday situations like the condensation of water vapor, the excess energy is carried away as heat to the environment. So there is a similar transfer of energy and entropy to the environment as in the case of life.

(* Equating structure and entropy is very hand-wavy and not always true. It seems to be wrong for Gravity but I don't know much about this.)

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Gold Member
2022 Award
Do you have a reference for this statement? I have never seen such a thing advanced as an "explanation" for the origin of life. Lots of things that, if they happened, would increase entropy, nevertheless fail to happen. So just saying that something increases entropy does not explain why that thing happened.
I think that's going back to Schrödinger's famous book "What is life".

Mentor
How can you explain the emergence of atoms and atomic bonding as processes that contribute to universal maximum entropy?
In a certain sense, yes.

As @Vanadium 50 pointed out, one usually does not consider entropy when dealing with individual systems. Instead, we look at energy. The hydrogen atom exists because the bound state between a proton and an electron has a lower energy than a separated proton and electron.

But why do systems tend to the lowest energy state? It is because of entropy. Lower the energy of an isolated system usually corresponds an increase in entropy. If a photon is emitted when the electron and the proton combine, then the entropy of the bound atom and the photon is greater than the entropy of the unbounded proton and electron alone.

There are situations where this is not the case. There was a time period in the early universe where stable atoms could not exist because the universe was too hot. Heck, there was even a time when protons themselves could not form (look up quark-gluon plasma).

EPR
You can 'explain' atoms( as per the title of the thread) by matter's perculiar states - from BEC on the lowest end of temperatures near the Absolute zero, to the plasma of the other end of the temperature spectrum(above 100 000 degress Celsium). Anything in between goes through phase transitions and symmetry breaking(what is usually termed 'solid'matter). Similar to the 3 much different states of water in varying temperatures. If the Universe was much much colder, atoms would likely behave quantum mechanically on our scale(is this last statement correct? Has Bose-Einstein condensate been realized with atoms of matter and not just gas?)

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Gold Member
2022 Award
In a certain sense, yes.

As @Vanadium 50 pointed out, one usually does not consider entropy when dealing with individual systems. Instead, we look at energy. The hydrogen atom exists because the bound state between a proton and an electron has a lower energy than a separated proton and electron.

But why do systems tend to the lowest energy state? It is because of entropy. Lower the energy of an isolated system usually corresponds an increase in entropy. If a photon is emitted when the electron and the proton combine, then the entropy of the bound atom and the photon is greater than the entropy of the unbounded proton and electron alone.

There are situations where this is not the case. There was a time period in the early universe where stable atoms could not exist because the universe was too hot. Heck, there was even a time when protons themselves could not form (look up quark-gluon plasma).
Well, it's a bit more subtle.

The entropy in the usual sense of (Gibbs) statistical mechanics is defined as (using natural units, where ##\hbar=c=k_{\text{B}}=1##)
$$S=-\mathrm{Tr} (\hat{\rho} \ln \hat{\rho}),$$
where ##\hat{\rho}## is the Statistical Operator of the system, representing the quantum state of this system.

Considering a system in a pure state, you have ##\hat{\rho}=|\psi \rangle \langle \psi|## you find ##S=0##. From an information-theoretical point of view this expresses the fact that within quantum theory a pure state represents a state of complete knowledge, i.e., you cannot specify a system "better" than by preparing it in a pure state.

Now consider a hydrogen atom. Here it depends on the level of sophistication you study it. Usually the first encounter is in the quantum-mechanics 1 lecture, where it is one of the few analytically solvable eigenvalue problem for the Hamilton operator taking into account only the Coulomb interaction between proton an electron. The energy eigenstates are the stationary states of a system and thus indeed of particular interest. That said makes immediately clear that when preparing a hydrogen atom (seen in this approximate way) in one of its energy eigenstates nothing happens to it, i.e., it stays in this state forever, i.e., as an isolated (closed) system it does not tend to relax to its ground state, i.e., the state of lowest energy.

Of course, this Hamiltonian is only a first approximation, which does not take into account many details, leading to the fine and hyperfine structure of its spectral lines. More important in our context is, however, that in fact the electromagnetic field itself is also a dynamical system, i.e., it is not merely providing the binding Coulomb potential for the electron and proton to a hydrogen atom but has to be quantized itself, and this enables the description of spontaneous emission of electromagnetic waves (or photons which is in this case really the adequate language, because spontaneous emission is the most obvious reason for the necessity of field quantization since it cannot be reliably described within semiclassical approaches). The quantization of the electromagnetic field leads to quantum fluctuations and the corresponding additional terms in a more complete Hamiltonian including the proton, electron, and the (quantized) electromagnetic field, which can be adequately treated in perturbation theory, leading to non-zero transition probabilities between the before calculated hydrogen energy eigenstates, and this implies that with some probability a hydrogen atom prepared in one of its excited states will emit a photon spontaneously bringing it to a lower energy eigenstate. Of course there are some selection rules concerning angular momentum, but the upshot is that indeed the hydrogen atom will relax to its ground state, which in this sense is the only really stationary state.