# Physicist Derives Laws of Thermodynamics For Life Itself

## The laws of thermodynamics must apply to self-replicating systems. Now one physicist has worked out how

Sep 10, 2012

Here’s an interesting thought experiment. Imagine a box filled with a variety of atoms and molecules in proportions roughly equivalent to the composition of the prebiotic soup in which life thrives.

How likely is it that these molecules will arrange themselves into fully-fledged living thing, a bacterium, for example? That’s a tough question but Jeremy England at the Massachusetts Institute of Technology in Cambridge has worked out how to calculate an answer, at least in theory. His results make for fascinating reading.

Part of the problem here is that life itself is hard to define. But England has a way round this. His idea is to examine every combination of states that are possible in this box and to consult an omniscient microbiologist about whether each state represents a bacterium or not. In that way, it ought to be possible, at least in principle, to gain an idea of the statistical physics involved.

Next, he asks the microbiologist to take another look at the box after a period that is roughly equivalent to the time it takes for bacteria to divide.

The question then is how likely is it that there will be two bacteria in the box.

Once again, the omniscient microbiologist could look at every possible state of the box and say whether or not self replication has taken place. If the box contains two bacterium, it’s possible to work how much entropy has been created in the process and how much heat used.

England throws in some basic laws of thermodynamics and in this way builds a statistical physics model of self replication, a model that is analogous to the laws that govern the statistical behaviour of any set of particles in a box.

By way of comparison, he also looks at the statistics that govern the reverse process–the spontaneous decomposition of the bacteria into carbon dioxide, hydrogen and so on.

This sets an important bound on what is thermodynamically possible in this system: in effect, England derives the second law of thermodynamics for the system. From this he works out various ‘laws’ such as the minimum amount of heat that a single round of cell division ought to produce.

Finally, he puts some numbers into his model, including figures such as the life time of peptide bonds in biological systems, to find out how much heat complex systems like E. coli bacteria ought to produce when they replicate.

It turns out that E. coli bacteria are remarkably efficient replicators. “The organism can convert chemical energy into a new copy of itself so efficiently that if it were to produce even half as much heat it would be pushing the limits of what is thermodynamically possible!” he says.

He does a similar calculation for the replication of RNA and DNA molecules. This suggests that in terms of thermodynamics, replication is  much easier for RNA than DNA.

That’s an interesting result given that many biologists have suggested that the first self-replicating systems in Earth’s pre-biotic soup must have been based on RNA rather than DNA

In the past, biologists have studied the catalytic properties of RNA that are crucial for living cells and noted that DNA does not share these properties. So the thinking is that RNA must have come first in the replicating timeline, with DNA evolving later as life became more complex .

England’s work backs up this idea but for completely different reasons–RNA is thermodynamically better at self replication. A fascinating result.

The work has an important limitation, however. It fails to tackle the definition of nature of life and instead defers the problem to an omniscient microbiologist who, it is assumed, can always provide an answer.

There is a tantalising hint that England’s approach could one day solve this problem. By exploring the role of statistical physics in more detail, it maybe possible to define life in terms of precise thermodynamic limits.

Which is why it’ll be worth watching where England takes his idea next.

Ref: arxiv.org/abs/1209.1179: Statistical Physics of Self-Replication