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The scientific contributions of Giorgio Parisi, who has won the 2021 Nobel Prize in physics, are so many that it would be impossible to mention all of them in a short piece.

As members of the Italian chapter of the Complex Systems Society, we would like to focus our attention only on stochastic resonance and the multifractal description of turbulence, two landmarks of complex physical systems that have proved particularly relevant for the study of the climate system – the overarching theme of this year’s Nobel prize motivation.

Usually, the concept of noise is associated with something negative, that one might want to reduce as much as possible. However, in the early 1980s, Parisi and collaborators discovered that when it comes to nonlinear physical systems such as the Earth’s climate, noise might play a positive role. This is due to a phenomenon known as stochastic resonance, observed in nonlinear systems where a characteristic frequency is present, for example in the form of a periodic perturbation. The right amount of noise can amplify the signal-to-noise ratio, favouring the emergence of a behaviour which would not be observed with a lower or higher noise level.

Stochastic resonance has been used to explain an apparent climatological paradox. For the last few million years, the average temperature on Earth has been strongly correlated with the flux of energy coming from the Sun, mostly due to the eccentricity of our planetary orbit. The variation of the energy flow is approximately periodic, with a characteristic period of about 100,000 years, but is too small to account for temperature variations of the order of 10 °C, such as those that can be reconstructed from the paleoclimatic record.

However, let’s also consider the internal dynamics of the ocean and the atmosphere (with periods of a few months and a few thousand years, respectively), which can be viewed as noise. It is possible to show that such noise, combined with periodic changes in the energy flow from the Sun, induces large variations of the global temperature which are roughly periodic. If one of those two ingredients, noise or periodic forcing, is absent, the phenomenon cannot hold. Curiously, Parisi’s article on stochastic resonance was rejected by top-tier journals such as Science and the Journal of Atmospheric Science. For almost a decade stochastic resonance was considered nothing more than a math curiosity, until it became clear that it characterizes many physical and biological systems. To date the article, published in 1982, has been cited thousands of times1.

Fully developed turbulence, i.e. the behavior of a fluid when the Reynolds number (the ratio of inertial to viscous forces) is very large and small-scale fluctuations become increasingly important, is another very complex phenomenon. It involves many degrees of freedom, spatio-temporal chaos, strong nonlinearity, and among other things, it is relevant for modelling the atmosphere and the climate.

A first description of the statistical features of these systems at small scales is due to Andrej Kolmogorov’s 1941 theory, also known as K41, whose results are in good (but not perfect) agreement with the observations. As noted by Lev Landau in a famous footnote in his 1959 book on fluids, K41 cannot be exact, because a unique exponent is used to describe how fluctuations vary at different spatial scales. In 1962 Kolmogorov proposed a refinement of his theory, followed by further investigation by Mandelbrot and Frisch in the 1970s, but there was still some disagreement between theoretical expectations and observations.

In the 1980s, Parisi and collaborators proposed a multifractal description2 3of fully developed turbulence, assuming that there is not a unique scaling exponent governing fluctuations, but a continuous spectrum of exponents, each belonging to a given fractal set. It is something less than a theory, but it allows precise predictions in terms of a unique ‘ingredient’ which can be estimated from experimental data. The multifractal description has had an important role in statistical physics, chaos and disordered systems, especially to elegantly clarify that the traditional paradigm was wrong, and that an infinite set of exponents is necessary for a complete characterization of fully developed turbulence.

In the early 1980s, those works involved very young researchers, the oldest being Giorgio Parisi himself (born in 1948) and the youngest being Giovanni Paladin (1958). It is worth wondering if, nowadays, such a group of physicists could exist at all: the time scales of academic research, especially in Italy, are now dramatically longer and young researchers are much less young, and more likely to spend time on grant writing and application-driven funded projects.

We hope that Giorgio’s Nobel Prize in Physics will attract the attention of funding institutions towards complex systems, because of their broad range of applicability from cells to societies and of how they stretch the current boundaries of physics. And that the Italian government will quickly increase the percentage of GDP spent on research to 3%, so that stories like this are not forever a thing of the past.