In 1943, one of the fathers of quantum mechanics, famous for his equation and his cat, Erwin Schrödinger, turned his attention to a problem that was seemingly simple but defied an easy answer. As World War 2 raged, he published a book titled What is Life?
Based on a series of lectures given in Dublin, the book’s theme was to answer the question: “how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?”
In other words: What is Life? Or, from a physicist’s point of view, how can life arise from inanimate matter.
Much of the lecture discussed the requirement for genetic material and some sort of encoding as well as how life related to thermodynamics — the laws governing energy, heat transport, and disorder.
Although their success largely depended on Rosalind Franklin’s X-ray diffraction experiments, Francis and Crick would also credit Schrödinger’s work for inspiring their research resulting in the discovery of the DNA double helix.
Schrödinger’s primary insight is that life creates order from disorder. In a universe governed by the 2nd law of thermodynamics, that all things tend to maximal disorder, living things maintain small enclaves of order within themselves. Moreover, if you look down to the atomic level, you find that the interiors of living things are extremely chaotic. Heat and molecules diffuse through rapid motion. Everything seems random. Yet the living thing persists, turning all that small scale chaos into large scale order.
Human built machines, by contrast, attempt to maintain order down to the smallest relevant levels. Microchips, for example, depend on orderly transfer of data down to nanometers. Precision machine tools, likewise, function because they have an exact specification at nearly the molecular level. The result is that human tools require careful protection and maintenance and break easily when subjected to the elements.
Life, on the other hand, has withstood the elements for billions of years precisely because it is able to build order out of chaos.
This has important implications not only for our understanding of biology but the future of human technology. If we are to build a lasting civilization, we must embrace the techniques that life has already developed to persist in a chaotic world. For that is the one rule by which life abides: Persist.
Despite an auspicious start, life eludes a clear definition that is scientifically measureable. Saying life turns chaos into order is all well and good, but you could say the same thing about crystals of salt formed from evaporation of sea water. Is a cycle of flooding and evaporation life? What about tornadoes and hurricanes? They are surely chaotic but also orderly. And they do persist for a time, longer than some single celled organisms and even insects.
What life needs is a clear mathematical definition, and statistical mechanics, the science dedicated to explaining macroscopic behavior from microscopic constituents, may be best suited science for the task.
Indeed, statistical mechanics already provides a clear connection between chaos at the molecular level and persistent, orderly phenomena at the macroscopic level. Measurements like temperature and pressure are emergent phenomena that, however precise and persistent they are, arise from the random motion of molecules.
Yet, this is insufficient for a true understanding of life because these macroscopic observations arise from gases and fluids that are in equilibrium. They do not change or if they do it is only from one equilibrium to another.
Life is different. It is not just order from chaos but order from chaos in motion. It is inherently not in equilibrium. For as soon as life reaches some equilibrium, it is dead.
Non-equilibrium statistical mechanics, which I will abbreviate NESM, however, can give a better answer. The key feature of NESM is to measure and quantify the probability of paths in phase space.
Phase space is simply a concept that physicists use to define the multidimensional space in which any system lives. Each dimension gives one measureable quantity of the system. For example, a one dimensional spring system has a two dimensional phase space: position and momentum. With those two numbers, you can quantify not only the exact state of the spring but, using the laws of physics, determine exactly where it is going and where it has been.
Most statistical systems have phase spaces in the millions of dimensions or more. We can even talk about infinite dimensional spaces where the measureable quantity is modeled as a smooth function or field. For example, an ocean or a river is made of so many particles that we might as well treat them as infinite and model the fluid using what is called a velocity field — basically a function that gives the velocity of a fluid for every position at the infinitesimal level.
Whether finite or infinite, Living things are complex enough to require large phase spaces. And every living thing moves through a phase space of some kind.
Phase spaces can also take into account when something loses and gains matter, as living things do as they eat, grow, and reproduce. It is a matter of characterizing every possible state the living thing will have during its life as a single point in the phase space.
Since living and non-living beings all move in phase spaces, the question is how to distinguish the motion of a living being versus a non-living thing in phase space. And this has to do with how a living being transitions from one point in phase space to another.
NESM does this for finite dimensional phase spaces through an equation called a Master equation, which defines the probability of transitioning from any point in phase space to any other point. In infinite dimensional phase spaces, the Master equation becomes a Langevin equation, which is similar to a differential equation, but it has some random noise added to it.
That is where the statistics comes in. Living things’ chaotic components at the microscopic level move so quickly and so chaotically we can model them as being entirely random fluctuations. Yet rather than suffering from those fluctuations, living things benefit from them, using them to transport signals, heat, and chemicals to where they need to go.
Using either a Master or Langevin equation it becomes possible to measure the probability of not only transitioning from one point to an adjacent point in phase space but to understand the probability of following a path in phase space from one point to another. This is called “trajectory” statistical mechanics.
This trajectory and the probability associated with it is theorized to distinguish life from non-life. The reason is that a living thing, by maintaining its internal order, is able to travel from one orderly point to another orderly one with a much higher probability than a non-living being in the same phase space. Likewise, it travels from an orderly point to a more disordered one with a much lower probability.
Moreover, living things can travel from point to point to point all while maintaining internal order because of the high probability that they maintain. Non-living things, on the other hand, travel from order to disorder to order in cycles. They will not do anything to break out of the cycle in order to persist. Thus, a living thing follows a more complex path in phase space than a non-living thing, avoiding paths to disorder if possible and also avoiding either static or cyclical equilibria.
This science is still very new. Unlike equilibrium systems, non-equilibrium (or what we sometimes call “far from” equilibrium) systems are poorly understood despite decades of documenting their behavior in both living and non-living things.
Fluctuation theorems such as Evans and Searles proved in 1994 show that systems can fluctuate away from equilibrium for short periods of time, actually violating the 2nd law of thermodynamics and effectively reversing time. But that is not what life is doing. The 2nd law only applies to isolated systems. Life interacts with an environment to “pump” disorder out like a heat pump pumps heat out of or into a house against the equilibrium order of things. Overall disorder increases but disorder inside the living organism decreases or stays the same.
Yet, non-equilibrium phenomena abound in the non-living world as well from snowflakes to stripes in the atmospheres of gas giants to hurricanes and tornadoes. All of these are ordered phenomena that persist for a time in a non-equilibrium state and then die out.
Inside a cell, all kinds of non-equilibrium phenomena are occurring such as DNA transcription, molecular motors, protein formation, and signaling. None of these in itself is alive yet together they maintain order within the cell and enable it to pass on its encoding. It is this ability to pass on an encoding and enable the life form to copy itself and thereby perpetuate that encoding that makes life truly unique. No tornado or salt crystal can do that.
One of the clear indicators of non-equilibrium processes that scientists have studied in single celled organisms is a loss of what is called detailed balance. Detailed balance is simply the sense that time is neither running forwards or backwards. In other words, a process is just as likely to move from one state in phase space to another as back again.
Thus, the trajectories through phase space that exemplify non-equilibria are those that are distinctly future oriented. They have a memory of past, and they are irreversible or nearly so. And these are also what life depends upon.