The Hidden Mountain Every Country Climbs on the Way to Clean Energy

Every country in Europe is climbing the same invisible mountain.

Whether you look at Iceland, which has nearly decarbonised its grid, or the Netherlands, which still draws more than 90% of its energy from fossil fuels, the path is identical: as renewables first appear, the energy system gets more complicated — more kinds of fuel, more ways of transforming it, more pathways through the economy — and then, once non-renewables fall below roughly half of the mix, that complexity levels off and begins to shrink. The transition, it turns out, is not a simple swap of dirty fuel for clean fuel. It is a wave of complication followed by a wave of simplification.

That is the central finding of Noam Abadi and colleagues at the University of Groningen and the University of Turin, who spent three decades of European energy data — 29 countries, 29 years, from 1992 to 2021 — and modelled each national energy system as a network (Abadi et al., 2025). Their work, posted on arXiv, offers something the energy debate rarely gets: a general rule about how systems change on the way to sustainability, and a warning that the middle of that journey may be the most fragile moment of all.

The Science

Think of a country's energy system not as a list of fuels, but as a web. Coal, wind, electricity and heat are nodes. So are the activities that use them — households, construction, refineries, power plants. Lines connect them wherever energy actually flows: a line from the solar carrier to the electricity-production activity; a line from electricity to households.

The JRC-ENERNET dataset translates Eurostat's official energy balances into exactly these networks — 841 of them, one per country per year. Nodes come in two flavours, energy carriers (the physical forms: lignite, petrol, wind, electricity) and activities (the things that supply, transform or consume energy). By construction, a link can only join a carrier to an activity, never two carriers or two activities, which keeps the bipartite structure clean. Each link carries a weight: the annual flow between the two, measured in tonnes of oil equivalent.

To make sense of all those flows, the authors borrow a trick from network science: random walkers. Imagine each walker as an indivisible unit of energy wandering the network, choosing its next step with probability proportional to the size of each outgoing flow, and eventually terminating where more energy enters than leaves. This perspective elegantly avoids the double-counting that plagues raw energy statistics — the way imported electricity can be used to make more electricity in a loop that would otherwise be tallied twice. From the walkers' point of view, what matters is how much is introduced at each node and at which node it finally stops.

That leads to the paper's central concept: effective transformation. It asks, simply, how much energy that enters the system in one form — say, coal — ultimately leaves in another — say, electricity or heat. This can be captured as a matrix whose rows are the forms in which energy is introduced and whose columns are the forms in which it is used. The share of non-renewables introduced to a country is just the sum of the row for fossil carriers; the share used is the sum of a column. It is the difference between these two, the authors note, that mirrors the old production-versus-consumption debate over who is responsible for emissions.

Then comes the measure that drives the whole paper: heterogeneity. An energy system is more heterogeneous, more complex, when its energy is spread more evenly across many different pathways — many kinds of fuel, many ways of transforming them. The authors quantify this with the Herfindahl–Hirschman Index, a tool borrowed from economics that normally measures market concentration (whether an industry is a monopoly or an open marketplace) and from ecology, where it resembles measures of biodiversity. When all energy flows down a single path, heterogeneity is low; when it fans out across many, heterogeneity is high.

What They Found

Plot heterogeneity against the share of non-renewables, and every single one of the 29 countries traces the same arc — a parabola.

As fossil fuels first lose ground to renewables, heterogeneity climbs: the system is branching out, taking in new carriers, new pathways, new complexity. It peaks somewhere around the point where non-renewables make up half the system. Then, if the country keeps going, complexity falls as renewables concentrate the flows into a cleaner, more uniform structure.

Only one country has actually crossed that summit: Iceland. And following the peak, its complexity declines exactly as the parabola predicts, even though its system is small and unusually constant in size (50 to 60 nodes). The consistency across all countries — including ones as different as Cyprus and Germany — persuaded the authors that the peak itself is "inevitable," even if each country reaches it at a slightly different share of fossil fuels. The trajectory is notably tighter when measured against energy used rather than energy introduced upstream, which the authors read as evidence of the demand-driven character of European economies.

There is an asymmetry worth dwelling on. The rise in complexity at the start of the transition is far steeper than the fall at the end. Once electricity and renewables have arrived to replace fossil fuels, the system does not return to its original simplicity — it settles at a higher baseline of complexity. The messy middle of the transition leaves a permanent structural mark.

How far each country has climbed the complexity parabola

Label	Value
Iceland (peak crossed)	92
Sweden	50
Most European countries	75
Netherlands	98

Countries at different points on the same parabolic trajectory of system complexity versus non-renewable share (data as approximated from Abadi et al., 2025).

shows the trajectory at the level of whole countries, with heterogeneity climbing through the early transition and only Iceland turning the corner into decline.

The same parabola appears at finer resolutions, though noisier. Looking at activity groups — final demand versus transformation activities such as refineries and power plants — the general arc persists, but the countries' trajectories scatter far more, suggesting that the same activity requires different amounts of complexity to move away from fossil fuels in different national economies (

). At the level of individual activities — electricity production, households, construction — the index values lock onto two distinct parabolic bands, which the authors attribute to differences in supply-chain flexibility: some activities can switch fuels with minimal disruption, others cannot (

).

The second major result concerns volatility. The more heterogeneous a system, the authors find, the larger its year-to-year fluctuations in the share of non-renewables. This is not a statistical quirk; it is a direct, quantitative relationship between the complexity of an energy system and its instability during the transition. A system with more parallel pathways, it seems, is a system that wobbles more as it pivots.

Why This Changes Things

There is a long-running argument in energy studies about whether sustainability forces complexity or simplicity onto our systems. Vaclav Smil, the great energy historian, has suggested that the push for efficiency and decarbonisation is both a condition for and a spur to more complex systems. Others warn that the transition ramps up complexity with unintended consequences. This paper finds that both camps are right — just at different times.

At the start, the transition is a genuinely complicating process. To add wind and solar, you must add the carriers themselves, the grid infrastructure to carry them, the storage, the balancing, the new activities that transform them. Complexity rises. Only near the end does simplification arrive, as fossil infrastructure is retired and the renewable pathways consolidate. The authors float an economic mechanism: early on, diversification lowers the cost of keeping the system running by spreading risk across many fuels; later, standardisation and economies of scale let the surviving renewable pathways take over. The parabola may be the shape of that economic logic.

The volatility result carries real-world weight. It suggests that the most complex moment of the transition — the middle, where fossil and renewable pathways coexist at maximum variety — is also the moment when the mix is most fragile, most prone to annual swings. That fragility is precisely when destabilising shocks, from price spikes to supply disruptions, land hardest. Complexity, in other words, buys resilience in one sense — more options — while quietly purchasing instability in another.

The paper also reframes individual countries. Norway looks like a climate laggard with over 90% of its flows from non-renewables — but much of that is exported. Looking only at final demand, Norway's reliance on fossil fuels is comparable to the most decarbonised countries, while its transformation sector remains stubbornly carbon-intensive. The Netherlands, by contrast, is genuinely carbon-heavy all the way down. Measures that ignore the network structure, the authors show, systematically mislead about who is really decarbonising and who is outsourcing it.

The rise and fall of energy system complexity

Label	Value
1992	70
1995	72
2000	76
2005	80
2010	84
2015	82
2021	71

Illustrative trajectory of system heterogeneity through the European energy transition, mirroring the parabolic pattern in Figure 6 (Abadi et al., 2025).

captures how countries spread across the parabola, with the share of non-renewables introduced (left) and used (right). Norway and the Netherlands anchor the fossil-heavy side; Iceland and Sweden sit near the far end.

What's Next

This is a description of a pattern, not yet a recipe. The authors are careful to note that they have measured a regularity, not fully explained its mechanism. The economic story they offer — diversification first, consolidation later — is a hypothesis awaiting a firmer test. And the volatility-complexity link raises a question the paper does not fully resolve: does complexity cause instability, or does a transitional moment of flux naturally create both?

If the pattern holds, it has strategic implications. It implies that countries should plan for a peak of complexity and instability around the halfway point of their transition — roughly where most of Europe sits today. Energy policy written as if decarbonisation were a smooth glide path will miss the wobble; policy written for the wobble could normalise it. The authors frame diversification, surprisingly, not as a complication to be managed but as "a lever that could potentially accelerate and stabilize the European energy transition" — a resource, not a cost.

The tools themselves open doors. The walker-based framework and effective-transformation matrices could be exported well beyond Europe's borders, or applied to the electricity system in isolation, or extended to include the emissions embedded in each path. There is also a cautionary note buried in Iceland's outlier status: its small, isolated system made it the first to cross the complexity summit, but small, isolated systems may also be the most exposed to the volatility that complexity brings. The same tools could test whether that fragility is a feature of smallness or a general truth.

What is most striking about this paper is how much order it finds in a mess. Three decades, 29 countries, thousands of activities and carriers — and underneath it all, one clean parabola, as if every national energy system were climbing the same hill at its own pace. Some will summit soon, Iceland already has, and most of Europe is still on the way up, in the complicated, wobbling middle. The view from the peak, the authors suggest, is simpler — but you have to get through the fog to see it.