How to detect life or did the omelet come before the egg

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Close your eyes. I give you 2 planets to hold, one in each hand. One harbors life as we know it, the other is without life. Which one would you say feels hotter in your palm? Why?

Detecting life on faraway planets is a gigantic an fascinating issue. We can’t just go there and look; we can’t even have a proper look from Earth. We have to rely on noisy measures that come from instruments very different from the sensors we’re used to in our own bodies.

An even more thorny issue is that we are not really sure how to define life.
I once heard someone say that a characteristic of life it that it goes against the 2nd law of thermodynamics (exploration of the relationship between life and entropy actually goes back to Erwin Schrodinger). My first reaction was disbelief, which is ironic considering that my first reaction to hearing the 2nd law in high school was also disbelief.
You might have heard it presented like this: if you break an egg and mix it up, you will never be able to get it back to its original state (separated white and yolk) even if you mix it forever. Why? Because of the 2nd law, which says that the universe must always go towards more disorder (actual formulation: The total entropy of an isolated system must always increase over time or remain constant.)
I strongly disliked the example of the egg, with its  fuzzy notion of “disorder”. I felt like the initial state was only special because my physics professor had decided so. What if I define another state as being special? I could record the position of each molecule after having mixed the egg for 20 seconds, and say that this is a very special state, and that any amount of mixing would not bring me back to that exact state. Therefore this sate must represent “order”. Then bringing the egg from its separated-white-and-yolk state to my special ordered state would be a decrease in entropy. The 2nd law did not make sense.

The notion of a relationship between an “order” and time made more sense in chemistry lessons, where everything “wants” to go to a state of lower energy. Electrons go to the lower orbits of the atom if they can find a free space. Spontaneous chemical reactions release energy, and non spontaneous ones require energy. And in mechanics, where everything also goes to the states of lower energy if given a chance. Balls go down hills, etc. But equating low energy with order in this way was just as wrong as my understanding of the egg example.

Entropy is a measure of statistical disorder. It is not applied to one state; it is the number of different microscopic states that a system could theoretically be in given a set of parameters. If you take cup of water, there is a given (enormous) number of positions at which each molecule can be: each one can be literally anywhere in the volume of the cup. If you now freeze the cup, each molecule has a reduced number of positions it could be in, because a crystal of ice has a specific structure and the molecules have to arrange themselves following that structure.
And here comes the relationship between entropy and beating an egg. The cup of ice has lower entropy than the cup of water. The non-beaten egg (each yolk particle must be in contact only with other yolk particles, except a fine layer; same for the white particles) has lower entropy than the beaten egg (each particle can be anywhere).

So what does it have to do with life? Consider the example of the egg. If it is such an organised structure, and the universe goes towards disorder, how could the atoms ever come together from a disorganised state and make such a highly organised, low entropy system as an egg? Order arising from disorder seems to defy the 2nd law. Entropy is sometimes defined as a measure of energy dispersal; does it mean that a planet with organised life everywhere would be colder than a planet without life?

It is mostly accepted that phenomenons seemingly going against the 2nd law do respect it when considered as part of a bigger system (there are several such cases besides life itself). You can make ordered ice from disordered water by channelling this disorder into the environment: it is the heat absorbed by your freezer. On average, the ice-freezer system still has the same entropy. So the egg must also come into existence at the expense of creating disorder somewhere else, and the 2nd law is respected. Maybe the 2 planets in our introduction would have the same average temperature.

These observations about the 2nd law and life do give us an interesting starting point to think about life definition and detection. You could say, like Lovelock when asked how to detect life on Mars, that entropy reduction is a characteristic of life.
But I would like to talk in terms of temporal patterns in energy. I haven’t really seen this discussed elsewhere, but I confess not having looked a lot either.

Life requires some chemical reactions to take place. Chemical reactions tend to have preferred directions: those that release energy and therefore lead to lower states of energy. If you want to obtain other reactions, you have to deliver energy to the system. In addition, if you want some reactions to happen at a predefined timing or in a specific order, you have to control when the energy is delivered to the system.
So, if you want to broaden the set of chemical reactions available to you, you need a way to store energy (and some other things to get proper metabolism: a way to get energy for storage, and a way to schedule the desired reactions).
If you store energy, it means that you are taking energy from your environment; it also means that you prevent this energy from being released.
Finally, because no energy transfer can be perfect, by causing chemical reactions to happen you must also be releasing heat in the environment.
So one way to detect life could be to look for pockets of stored energy and heat that are isolated from the environment.

Back to our introduction, which planet would be hotter and why?
Consider what makes the basis of life on Earth: plants. Plants feed on sunlight, animals feed on plants, other animals feed on animals that feed on plants.
Plants use solar energy for immediate chemical reactions; they also use it to store energy in starch form. Without plants a lot of this energy would just disperse back into the atmosphere and back in space. Animals eat the plants, and in turn store energy. Of course, they also disperse some of the energy. But for an organism to survive, the total of the dispersed energy must always be less than the stored energy; even if energy is necessary to hunt and digest preys (the sources of energy). Natural selection must favor efficient storage.

Clearly, a planet where life depends heavily on sunlight must harbor more energy than a planet without life. The problem is that some (a lot? How much? Why?) of this energy is stored, and passes from one form of storage to another. The planet would only be hotter if life consistently releases more energy than is currently being absorbed from outside into stored form, that is, releasing energy that had been stored in the past and not used (for example, animals eating a stock of very old trees, or humans burning fossile fuels). Obviously, that kind of situation can only go on as long as the stock of “old” energy lasts, so it is only a temporary state. Therefore we should try to measure stored energy, not the energy being currently dispersed in heat form, which is what temperature measures.

Unfortunately, the only way to measure how much energy is stored somewhere without having access to the history of the object is to burn it down and see how much energy is released in heat form. Burning down entire planets is not a very convenient way to proceed. We are better off looking for indirect signs that energy might be stored somewhere, by detecting small pockets of variable heat isolated from sources of constant heat.

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