Thoughts

Why do structures emerge?

Behind much of the physics I work on lies a question that seems more fundamental to me than any of the particular phenomena we study: why does matter, when driven far from equilibrium, not simply dissipate the energy it receives, but instead give rise to patterns, correlations, broken symmetries, domains, networks, and characteristic scales? Why can a transient excitation give rise to order that outlives the excitation itself?

A pulse of light reaching a surface, with a lattice and a spiral emerging from the disorder — A pulse arrives, the energy spreads through electrons, phonons and defects, and something ordered is left behind. The subject of this page is the middle step, the one that decides which order.

What makes the question unsettling is that these forms of order are usually not imposed from outside. They emerge. They arise from the interaction of a very large number of degrees of freedom, each obeying comparatively simple local rules, none of which knows what global organization is supposed to appear. That may be one of the great conceptual problems of physics: understanding how microscopic laws give rise to collective behaviours that are not obviously contained in their elementary description.

In the systems I study, a laser pulse deposits energy in a solid within a few femtoseconds. The excitation initially resides in a very small subset of the system’s degrees of freedom, before spreading through its electronic, vibrational, structural, and electromagnetic degrees of freedom. The energy redistributes. Instabilities emerge. Some fluctuations are amplified, others decay. Spatial scales are selected. Patterns can eventually emerge.

What interests me, therefore, is not only what emerges, but why it emerges. Why this wavelength rather than another? Why this symmetry? Why this collective dynamics? Why this particular organization among the immense number of configurations accessible at the microscopic level?

A hierarchy that works, and a step that stays mysterious

Physics has built a remarkably effective hierarchy of descriptions: particles, atoms, electrons, collective excitations, phases of matter, mesoscopic objects, macroscopic structures. At each scale, relevant variables emerge, along with their own symmetries and effective laws. Yet something remains obscure in the passage from one level to the next: how does a new description emerge from the one beneath it?

A microscopic description can be perfectly deterministic without revealing the macroscopic order it will produce. Conversely, remarkably complex behaviours can be governed by a surprisingly small number of collective variables. Complexity is not simply a matter of how many constituents a system contains. It lies in how their degrees of freedom organize themselves within a given environment.

Large-scale projection through the Illustris simulation centred on the most massive galaxy cluster — Large-scale projection from the Illustris simulation at the present epoch, centred on the most massive galaxy cluster. The image transitions from dark matter density on the left to gas density on the right. Filaments, sheets, and voids are nowhere to be found in the initial conditions: they emerge through the action of gravity on tiny fluctuations. Image © Heidelberg Institute for Theoretical Studies (HITS), reproduced from the Gauss Centre for Supercomputing.

That raises a question about the status of physical laws themselves.

Are the fundamental laws only those that govern the elementary constituents? Or does each level of organization bring its own principles, becoming relevant as new scales and degrees of freedom emerge? One of the deepest lessons of modern physics may be that the second possibility does not contradict the first. Laws can be universal, while the phenomena they generate are not.

What emergence actually means

An emergent phenomenon is not simply a complicated one. It is a collective organization whose relevant properties cannot be reduced to those of its constituents taken individually.

An electron carries energy, but not a temperature.
A single atom does not have a phase.
A fluctuation does not contain the pattern it may eventually seed.
A single degree of freedom does not define a characteristic scale.

And yet these phenomena are physically real. They emerge when many degrees of freedom interact, when fluctuations are amplified or suppressed, and when new scales separate from the microscopic ones. Nature can produce something genuinely new without introducing new constituents, simply by reorganizing the ones already there.

The new is not necessarily hidden in the parts. It can emerge from the way the parts interact.

France seen at night from orbit, with cities forming a network of lit nodes and filaments — **A network nobody designed as a whole.** France at night seen from orbit. No single decision produced this pattern: it is the accumulated result of local constraints, rivers, coasts, roads, historical accidents, and it nevertheless shows a characteristic spacing, a hierarchy of nodes and filaments that connect them. Image courtesy of NASA Earth Observatory.

This leads to an intuition that guides part of my research: perhaps complexity is better understood not by accumulating microscopic detail, but by identifying the selection mechanisms that progressively eliminate the vast majority of possible configurations. A structure that emerges spontaneously is physical information. It tells us that, among all the configurations compatible with the constituents and constraints, some are dynamically privileged. Understanding a structure is therefore not simply a matter of showing that it can exist. It is understanding why the dynamics selects some configurations over others. And that selection can be deeply universal.

Why far from equilibrium

What fascinates me about systems far from equilibrium is precisely that they force this question on us without allowing us to take refuge in equilibrium thermodynamics. At equilibrium, powerful principles often tell us which states are favoured: free-energy minimization, entropy maximization, and symmetry. Far from equilibrium, the situation is much less comfortable. There is generally no single state function that tells us in advance which organization will emerge.

And yet order does emerge. Structures form, move, are selected, interact, and disappear. Microscopic fluctuations can be amplified until they become macroscopic features. Order is therefore not necessarily the opposite of disorder. It can emerge as a dynamical consequence of dissipation. That is perhaps why systems far from equilibrium are so rich: they show us matter not as it is, but as it becomes.

Order is not necessarily the opposite of disorder. It can be a dynamical property of dissipation.

What a structure is telling us

The ultimate question might then be this: what is nature telling us when order emerges? Nature is, of course, not trying to tell us anything in the literal sense. But the phenomena we observe are visible traces of deeper constraints. They reveal something about the interactions, symmetries, timescales, energy fluxes, and degrees of freedom that govern the system.

Perhaps every emergent phenomenon is a kind of message, not encoded in its details but in the relations it establishes between scales. A pattern tells us that a scale has become relevant. A broken symmetry tells us that a fluctuation has been amplified. A collective organization tells us that interactions have overtaken individual behaviour. An invariance tells us that part of the microscopic detail has become irrelevant. Emergent phenomena may then be less like objects than like fingerprints of the underlying laws.

This is the perspective from which I look at the phenomena I study. The patterns created by a laser pulse, the ultrafast transitions, the surface instabilities, and the collective dynamics are not only particular phenomena. They are natural experiments in which matter reveals, on timescales and length scales we can actually reach, some of the mechanisms through which complexity and collective behaviour emerge.

The question that interests me in the end is therefore broader than any single material or technique: how do simple laws give rise to complex behaviour? And perhaps, more deeply still: is there a theory of emergence as universal as the laws from which these phenomena arise? I do not know whether such a theory exists. But it may be exactly the right question to ask.