Ok but people have known this for more than 100 years. What they didn’t know for certain until the 90’s, however, was that this statement is true whether or not a system is in thermal equilibrium with its surroundings. This is another topic for another time, but deriving statements that are true for systems arbitrarily displaced from equilibrium is HARD. Ilya Prigogine got a nobel prize for writing down expressions for the time-derivatives of the entropy change in what is called a “near-equilibrium regime.” Up until recently, and if you ask the opinions of older thermodynamicists still today, a common viewpoint is that nothing persuasive can be said generally about non-equilibrium systems and that their unpredictable dynamics just lie entirely outside the time-reversible world of mechanics. Happily, this view is receding and England’s work will hopefully be a major step forward in popularizing non-equilibrium ideas in the larger scientific community.

Ok so the fluctuation theorem isn’t restricted to equilibrium systems: so what? Well that means that it has general validity for any macroscopic process that we can succesfully represent in terms of a macrostate/microstate scheme. Among those schemes are the macrostates, “a jar containing one bacteria” and “a jar containing two bacteria.” You can read the paper for yourself, I think its fairly accessible if you don’t get hung up on the math notation. The summary is that using this coarse-graining scheme England is able to perform a calculation of the minimum entropy that must be produced during a bacterial replication process, and it turns out that e. coli are clearly very close to being perfect replicating machines. This is a wonderful result, but two points in the paper, for me, are more interesting than the calculation itself.