Friday, 25 September 2026

Schrödinger Re-Revisited: Long Live Negentropy!

I confess that before posting this here, I tried to publish it as a letter to the editor in a major bioengineering journal. Despite a preliminary check with the Editor-in-Chief, the associate editor returned it to me because it was not an original article. It is not; it is an opinion piece, so I gave up and posted it here. 

As biomedical engineers, we are constantly pulled in two opposing directions, epistemologically speaking: on one side, toward physics and its universal theories, such as quantum mechanics and general relativity, whose laws govern even living organisms; on the other, toward biology, with all its complexity, its constant subjection to moral scrutiny, and its lingering remnants of vitalism.  Especially now that technologies such as in silico medicine are making the contradictions between Bayesian and Frequentist inference more evident, these opposing pulls can be very strong.

One of the first to try to bridge this gap was Erwin Schrödinger in his book “What Is Life? The Physical Aspect of the Living Cell. Cambridge: Cambridge University Press, 1944”.

I recently read Carlo Rovelli’s popular science book (Sull'eguaglianza di tutte le cose. Lezioni americane. Adelphi, 2025; here also the English version); strongly recommended.  A footnote in a book led me to a paper I missed at the time of publication: Jeffery, K., Pollack, R., & Rovelli, C. (2019). On the statistical mechanics of life: Schrödinger revisited. Entropy, 21(12), 1211. https://doi.org/10.3390/e21121211.

In it, the authors argue against the idea that, in a closed system, an increase in entropy must always be associated with an increase in disorder.  They do this by separating the macroscopic order from the microscopic one and by defining order as correlations in time and space, meaning that particles or phenomena in the universe are not randomly dispersed but rather exhibit spatial or temporal structure.

Using this perspective, they challenge the idea of living organisms as producers of negative entropy, or negentropy:  “This leads us to a perspective on the possible statistical underpinning of life, whereby life is not an improbable “fight against entropy” —as Erwin Schrödinger famously put it in his adventure into biology (Schrödinger 1944)— but is rather a statistically favoured process directly driven by entropy growth, in which movement of a system within a space of available states leads it to discover —and traverse — channels between metastable states”.

At the end of the paper, I could not find anything wrong in what the authors wrote, but still, I was left with a sense that something was missing.  It took me some thinking to understand what it was.

The authors’ argument is that living systems follow their “thermodynamic destiny” like any other inanimate matter, but because of the inherent complexity of carbon-based chemistry, there are systems with a huge number of degrees of freedom, and as such, they may persist for long periods in regions of the phase space with lower probability (and lower entropy), which they call metastable states.  The transition between a metastable state and another is a low-probability event, allowed by what they call channels, for example, the formation of an enzyme that allows chemical reactions that would have been otherwise impossible.  All this is coherent with the “Rovelli thinking”, which he presented in many publications, including some very successful popular science books. 

I am not a theoretical physicist, but from where I stand, all this makes sense. But I believe it is missing something that Schrödinger’s Negentropy was trying to capture.

The terms teleology and teleonomy both describe apparent “purpose”, but they mean different things, especially in biology. Teleology explains something in terms of its end, goal, or purpose. For example: “Birds have wings in order to fly.” Taken literally, this can imply that evolution or nature is directed toward a predetermined goal. Teleonomy describes goal-directed-looking organisation without assuming foresight or a predetermined cosmic purpose. In biology, wings serve the function of flight because natural selection preserved traits that improved reproductive success—not because evolution was consciously aiming at flight.

I think most biomedical scientists today accept that the teleology of living systems is only apparent; it is indeed a teleonomy. But despite this, we all keep using teleonomic narratives.  Why?  In part, I am sure there are some leftover needs of vitalism, the need to treat life as something apart from the rest of nature. But there is another reason: teleonomic narratives work.  In a number of cases, assuming there is some agency in the behaviour of living organisms, helps a lot in unravelling complex processes. 

The reason for this, I believe, is that natural selection is such a totalising driving force that it appears purposeful. We accept that evolution is a blind process, driven only by some ecological rules.  But such rules produce a “sense of purpose” so strong that it helps to understand most biological processes.

I teach my students that one of the primary ways animals use to decide if something is alive is if it moves with purpose. Of course, this is not a law; robotic vacuum cleaners move with purpose but are not alive. But in nature, it is a pretty good rule of thumb. A stone has no agency; most living creatures do.

They do have agency, not because they are fundamentally different from a stone, but because they are enormously more complex systems than a stone, and because they are the result of natural selection, which favours certain trajectories in their phase space, those that increase chances of reproduction.

The difference between Schrödinger’s “improbable” fight against entropy and Rovelli’s statistically favoured process, directly driven by entropy growth, traversing channels between metastable states, is here.  I think we can easily accept that the fundamental thermodynamic principles that regulate living organisms are not fundamentally different from those regulating inanimate things.

But the fact that among all the infinite molecular configurations possible, neurons evolved so that when an action potential depolarises their axon, voltage-gated Na⁺ channels inactivate and voltage-gated K⁺ channels open, K⁺ flows out of the axon, making the inside more negative again, returning the membrane potential toward its repolarised resting value, is amazing, to say the least. The negentropy narrative helps us to capture that amazing teleonomy that natural selection brought into this.

I appreciate that from a theoretical physics perspective, Rovelli’s narrative is more rigorous. But from a biological perspective, it is quite unhelpful.  Negentropy, with all its limits, is functional to the agency that we should not neglect when investigating life. 

Thursday, 3 September 2026

One foot in, one foot out

When I was much younger, I learnt that complex, delicate things such as love, once they break down, cannot be truly fixed. It is an irreversible operation, as I learned a few years later while studying physics. 

Today I realised that stopping doing research is also an irreversible operation. 

Being an active scientific researcher means you are part of small communities of peers debating a research topic in near real time through papers and conferences.

In Sheffield, in one of the University buildings, there is a Paternoster lift, a continuously moving, doorless passenger elevator that loops up and down on a shared chain without ever stopping.  I always hated the thing; it scared me. And every time I had to step into it, I would hesitate for a little while, enough for the car to move too high to get in, so I had to wait for the next car. 

Research is a bit like this: you have to stay in the loop.  If you step out, even for only a minute, everyone else moves on, and you cannot catch up.  Or, to be more precise, to catch up, you have to make a huge effort just to return to where you were before you left; I am sure everyone who has experienced a long sick leave or maternity leave can relate. But in my case, I stopped doing research not only because of an external factor (a health problem) but also because I was tired. Even if I wanted to, I would not have the energy to catch up.

Why this rant? Yesterday, the VPH2026 conference started in Milan. VPH stands for Virtual Physiological Human, the name the European Commission gave to the very first funding stream in this research domain. Today, we call it in silico medicine.  For those who do not know me, I co-authored the white paper that in 2005 proposed the term VPH; in 2007, I was the editor of the first research roadmap; In 2011, I founded the VPH Institute (now VPH Society) that represents academic research, and in 2016, the Avicenna Alliance, which represents industrial research. Also, I co-founded and directed the Insigneo Institute for in silico medicine from 2012 to 2018.  At the conference, there are 600 delegates; I bet I know half of them personally. And with many of them, I shared much of my life, and I consider them friends.

So, some time ago, I realised that I had to show up at an event with so many friends, only a one-hour train ride from where I live. And today I did.  

It was nice to see so many friends from all over the world, and I was delighted to see that this crazy idea we had that the computer models could help cure people today is a solid reality.

But as I attended the lectures, as I had a million times before, I felt something was wrong.   Some introspection brought me here: it was like being in the Paternoster car with one foot in and one out.  I was listening to and understanding most of what was said, but I was not as involved as I was before.

Now I am writing this on the train that takes me back home. As I do, I realised that this is an irreversible decision; once you are out, you are out for good.  Much of what I learned over 40 years in my profession will not become obsolete tomorrow, so I can still teach, mentor, and write popular science. But doing research is over.

When a love ends, you are usually sad, even if you broke up; you miss the good things that love gave you.  Right now, I am sad. I had a true passion in my life, and now it is gone. 

But one thing old age teaches you is that life is all about loss.  When it happens, you cry a little, you remember the good days (but not too much, or you will live in the past), and then you move on.  There is a lot more to lose in front of you.