Phase transitions
Why change is sometimes abrupt, and what that means for recognising it.
A phase transition is a sudden, qualitative change in the behaviour of a system. Water freezing is the best-known example. A population tipping into collective action, or a patient who deteriorates or recovers rather suddenly, can also go through such a transition.
In physics one also speaks of a tipping point or a bifurcation. The catastrophe theory of René Thom and Christopher Zeeman provides a mathematical description of it. In psychology, Günter Schiepek has worked for decades on making such transitions in psychotherapy measurable.
First-order and second-order phase transitions
Not all phase transitions are equally abrupt. A first-order phase transition is the sharp variant: at a certain temperature, pressure or load the system tips all at once, like water at 0°C or 100°C, or a ruler that is compressed harder and harder and at a certain moment suddenly buckles sideways. A depression, too, can sometimes shift within a few days from deep despair to renewed energy, or in the opposite direction.
A second-order phase transition is more gradual. The system changes character step by step, without any single moment standing out as the shift. Many developmental processes seem to be of this type. Comparing the system before and after the transition, one nevertheless sees that it has become something qualitatively different.
Hysteresis: there and back are not the same
A striking feature of many phase transitions is hysteresis: the tipping point on the way there does not lie in the same place as the tipping point on the way back. Marten Scheffer's classic example is that of shallow lakes. As the phosphorus load increases, a clear lake tips into a turbid one. To make it clear again, however, the phosphorus load has to be brought down much further than the original tipping point, sometimes so far that this is not achievable in practice.
"The dogma that the cause of the problem is the key to its solution does not necessarily hold for complex systems." (Van der Maas, 2024)
For depression and other chronic conditions, this is an important consideration. A system that once slipped into a depressive state under the influence of stress does not automatically return to the healthy state when the stress diminishes. Hysteresis then works against recovery. It may be necessary to go further than seems logical or, as with the lakes, to look for an altogether different intervention (in the lakes, this was removing fish rather than reducing phosphorus further).
Early warning signals
One of the most interesting findings in research on phase transitions is that they often announce themselves. Shortly before a system shifts, it shows characteristic signals, which we call early warning signals or critical slowing down: the system recovers more slowly from small disturbances, variance increases, autocorrelation rises and fluctuations become slower.
For the consulting room, this means that it is in principle possible to see in a patient's time series data whether a phase transition is approaching. Sometimes it concerns an improvement that is on its way, sometimes a relapse that is announcing itself. The so-called catastrophe flags (sudden jump, multimodality, divergence, hysteresis, critical slowing down and a few others) are methodological tools for detecting this in real data.
Perhaps the most important lesson is that change need not be gradual. In the consulting room we often think in terms of dose and response: more therapy, more recovery. With phase transitions things may go differently, with little visible effect for a long time and then, suddenly, a jump. Keeping this in mind makes it less likely that one concludes too soon that a treatment is not working, and makes it easier to be patient until the moment arrives.