Abstracts
Abstracts
(CNR-ISMAR and INGV, Roma)
The deep ocean dynamics from observations, parameterizations and models.
The exchange between the ocean's turbulent surface boundary layer and the underlying stratified water column can occur over a wide range of timescales. On the other hand, deep water takes many decades to return to the surface, acting as reservoir of heat and CO2, contributing to the climate decadal variability. The bottom dynamics has been re-evaluated in recent papers, in which the interplay between downward and upward energy propagation has updated the original vision of Munk (1966). The Mediterranean basins is as a good example to explore this physical (upside-down) mechanism. Recently, in the Ionian Sea, a significant positive shift of the ocean heat content between 2000 and 4000 m has been observed in the last decades. This intriguing heat storage is due to the bottom-driven mixing processes, produced by the ventilation of the deep layers of two different deep-water sources, originating from the Adriatic and the Aegean, respectively. From the above, we intend to discuss the role of the deep mixing in the abyssal circulation in the Mediterranean Sea, considering new in situ data exploring the deep dynamics and modeling results.
Artale V., et al., Linking mixing processes and climate variability to the heat content distribution of the Eastern Mediterranean abyss, Sci. Rep. 8 (1) (2018) 11317.
Ferrari R., et al., Turning Ocean Mixing Upside Down, J. Phys. Oceanogr. 46 (2016).
Giambenedetti B., et al., Multi-approach analysis of baroclinic internal tide perturbation in the Ionian sea abyssal layer (mediterranean sea), Geophys. Res. Lett. (2023).
Klein B., et al., The large deep-water transient in the Eastern Mediterranean, Deep Sea Res. Part I Oceanogr. Res. Pap. 46 (3) (1999) 371–414.
Kunze E., et al., Turbulent Mixing and Exchange with Interior Waters on Sloping Boundaries, J. Phys. Oceanogr. 42 (6) (2012) 910–927.
Munk W., Abyssal Recipes, Deep-Sea Res. Oceanogr. Abstracts 13 (4) (1966) 707–730.
Wunsch C., R. Ferrari, Vertical mixing, energy, and the general circulation of the oceans., Annu. Rev. Fluid Mech. 36 (1) (2004) 281–314.
Motion in bounded domains represents a paradigm in several settings: from billiard dynamics to random walks on a finite lattice, with applications to relevant physical, ecological and biological problems: a remarkable universal property, involving the average of return times to the boundary, has been recently proposed. Here mechanisms that lead to violations of universality, induced by boundary effects, are discussed, and they are related to the spatial structure of the invariant measure.
How much entanglement is there between two modes in a random quantum state?
Don Page in a celebrated paper of now 30+ years ago showed that if quantum system is made up of two parts of dimensionality M and N, and the joint state is pure, then the entanglement entropy of the smaller system (say N) is almost surely maximal, in the limit when the dimension of the larger system (say M) becomes very large. That is, a small subsystem behaves almost surely as if it were thermal and at infinite temperature, if the joint state over the smaller and the larger system is picked randomly (sampled w r t the Haar measure on unitary transformation acting on a reference state). We recently looked at entanglement between two modes where the state of each mode is fixed to be thermal at finite temperature (Aurell et al, PRL 133:060202 (2024)). To make headway we assumed that the total state is not only pure but also Gaussian. We hence looked at the entanglement between two modes in a random Gaussian state with fixed 1-mode marginals: under suitable limits two such modes are almost surely not entangled. One can thus have a total pure (and Gaussian) state mimic a total thermal state, both for the single-mode marginals, and for mode-mode entanglement.
One amusing application of these random matrix calculations is to a problem Angelo and his co-authors explicitly excluded from their Random Walk in Physics: Hawking radiation from a black hole. While nobody knows exactly how this radiation looks like (or if it even exists), we can say that it is no problem for quantum mechanics if all the mode marginals are thermal (as Hawking predicted) and if all the mode-mode entanglement is zero (as he and Wald predicted for particles emitted from the black hole at about the same time). In another direction, the theory of constrained randomized symplectic transformations which we developed may be relevant to how a non-ergodic system may look ergodic to an observer who only has access to a part of the system, a problem recently addressed by Angelo and collaborators in several papers.
It is a pleasure and an honor to dedicate this talk to Angelo, a man of profound and broad learning and with a subtle mind, who has born both lightly throughout life, but who never managed to hide either from his friends who love him.
The success of Statistical Mechanics in describing the equilibrium behaviour of macroscopic systems is often ascribed to the chaotic nature of the underlying microscopic dynamics, which guarantees ergodicity. In this respect, integrable systems should be regarded as pathological, since the presence of an extensive number of conserved quantities prevents the dynamics from being ergodic. Nonetheless, empirical evidence suggests that relevant macroscopic observables typically follow a good thermodynamic behavior even for this class of models.
Recent works [1-4] have investigated numerically and analytically the thermalization properties of paradigmatic integrable systems in the classical domain, such as the harmonic chain, the Toda model, and some classes of disordered harmonic systems. The main finding is that thermalization is typical, even when the system is prepared in far-from-equilibrium initial conditions, provided that the considered observable has a global nature and the total number of degrees of freedom is large. The reason for this behaviour lies in the dephasing of normal modes, which is responsible for an "effective" ergodicity. Our results support the scenario proposed by Khinchin to give mathematical foundations to the Statistical Mechanics of large non-interacting systems.
[1] M. B., A. Vulpiani, G. Gradenigo, "Statistical Mechanics of an Integrable System", J Stat Phys 183, 41 (2021)
[2] N. Cocciaglia, A. Vulpiani, G. Gradenigo, "Thermalization without chaos in harmonic systems", Physica A 601, 127581 (2022)
[3] M. B., R. Marino, A. Vulpiani, "Ergodic observables in non-ergodic systems: The example of the harmonic chain", Physica A 630, 129273 (2023)
[4] M. Cattaneo, M. B., D. Lucente, P. Muratore-Ginanneschi, A. Vulpiani, "Thermalization is typical in large classical and quantum harmonic systems", in preparation
(Università Tor Vergata, Roma)
Turbulence with Emulsion
In this talk, I discuss recent studies about turbulence with stable emulsion. In particular I will focus on the onset of stable convection and three dimensional homogeneous and isotropic turbulence. By varying the volume fraction, several new features appear and eventually a phase inversion occurs in the system.
The wave counterparts of the classical paths of material particles and the rays of geometrical optics are trajectories modified by a ‘quantum potential’. Wave interference corresponds to undulations in these trajectories Trajectories are strongly influenced by phase singularities (aka wave vortices) and stagnation points. The local quantum velocity (proportional to the phase gradient of the wavefunction) can be faster than the classically allowed speed. This is an example of superoscillations, in regions bounded by zeros of the quantum potential. In the quantum generalisation of classical curl forces (accelerations that are not the gradient of a potential), the canonical and kinetic velocities are different. Some curl forces involve Hamiltonians anisotropic in momentum, with unfamiliar quantum mechanics.
(Università Tor Vergata, Roma)
We present a stochastic method for generating and reconstructing complex signals along the trajectories of small objects passively advected by turbulent flows [1]. Our approach makes use of generative Diffusion Models, a recently proposed data-driven machine learning technique. We show applications to 3D tracers and inertial particles in highly turbulent flows, 2D trajectories from NOAA’s Global Drifter Program and dynamics of charged particles in astrophysics. Supremacy against linear decomposition and Gaussian Regression Processes is analyzed in terms of statistical and point-wise metrics concerning intermittency and multi-scale properties. Preliminary results concerning generalizability and model collapse will also be discussed. [1] Li, T., Biferale, L., Bonaccorso, F. et al. Synthetic Lagrangian turbulence by generative diffusion models. Nat Mach Intell 6, 393–403 (2024).
(LINS, University of Paris-Saclay)
Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective models. Causal analysis can be viewed from two different angles: Intervention causality and Observation causality. We are interested in interventional causality, which focuses on examining the causal effects of interventions or treatments. It aims to answer questions such as ”What is the impact of a particular intervention on a particular outcome of interest?”
Recently, this problem has been tackled in the response theory framework, and it has been shown that the generalized response of the system points to the interventional causality. However, in practice the physical model of many phenomena is not known, and deciphering causal relationships from observational data is a difficult task, as correlations alone may not provide definitive evidence of causality.
In this talk, we consider two paradigmatic physical exemples, namely a linear markov system with a nonlinear potential perturbation, and the fully nonlinear chaotic Lorenz model. We analyze how state-of-the-art machine learning tools based on neural networks compare against ground truth interventional causal response, and the linear approximation.
Our results show that, while the linear case may be considered somewhat simple and may be learnt, the full nonlinear case is difficult and presents many subtleties. In particular, even if specific neural networks are able to accurately reconstruct the phase-space, and notably auto-correlations of the state variables, the prediction of the response may largely fail in some cases. This is due to the fact that the response is related to two-point statistics, and the system is chaotic.
When machine learning can leverage some physical a priori of the system, results are improved.
(Università della Campania “Luigi Vanvitelli”, Napoli)
The understanding of the fundamental relation between electrophysiological activity and brain organization with respect to performing even simple tasks is a long-standing fascinating question. Recent experiments have shown that the spontaneous brain activity is characterized by avalanches showing absence of characteristic size, result successfully interpreted in the context of criticality. The fundamental open question of the relation between spontaneous and evoked activity is addressed by means of the stochastic Wilson Cowan model. An approach inspired in non-equilibrium statistical physics allows to derive fluctuation-dissipation relations, suggesting that measurements of the spontaneous fluctuations in the global brain activity alone could provide a prediction for the system response to a stimulus. Theoretical predictions are in good agreement with MEG data for healthy patients performing visual tasks. The analysis is performed in a wide range of parameters, setting the system at and off criticality.
(CNRS, SPEC, University Paris-Saclay)
We discuss how projection of geophysical equations of motion onto an exponential grid
allows to achieve realistic values of parameters, at a moderate cost. This allows to perform many simulations over a wide range of parameters, thereby leading to general scaling laws of transport efficiency that can then be used to parametrize the turbulent transport in general climate models for Earth or other planets.
We illustrate this process using the equation describing the heat transport in a dry atmosphere, to obtain the scaling laws for onset of convection as a function of rotation.
We confirm the theoretical scaling of the critical Rayleigh number $\Ra_c\sim E^{-4/3}$
over a wide range of parameter.
We have also demonstrated the existence of two regimes of convection, one laminar extending near the convection onset, and one turbulent, occurring as soon as the vertical Reynolds number reaches a value of $10^4$.
We derive general scaling laws for these two regimes, both for transport of heat, dissipation of kinetic energy, and value of the anisotropy and temperature fluctuations
(John Hopkins University, Baltimore)
Non-Equilibrium Giant Concentration Fluctuations and the Kraichnan Model
Certain crucial experiments have reshaped our understanding of nature, e.g. the 1908 experiment of Perrin on the determination of Avogadro’s number from observations of Brownian particles convinced the physics community of the reality of atoms. We argue that the experimental observation of non-equilibrium giant concentration fluctuations in liquid diffusion, by Alberto Vailati and others, may play a similar crucial role. These experiments show that such non-equilibrium thermal fluctuations in the presence of a concentration gradient are orders of magnitude larger than equilibrium fluctuations. In fact, these fluctuations, in the absence of gravity, propagate up to the fluid domain size! These large, macroscopic fluctuations are typical, not rare, and are not explained by the deterministic diffusion equation but instead by Landau-Lifschitz fluctuating hydrodynamics of a binary fluid mixture. Donev, Fai and vanden-Eijnden (DFV) in 2014 developed a high-Schmidt asymptotic theory whch reduces to a version of the Kraichnan model of random advection, in which the concentration fluctuations are nonlinearly advected by thermal velocity fluctuations. This theory yields the Stokes-Einstein relation for liquid diffusion as an ``eddy-diffusivity’' effect of the thermal velocity fluctuations and describes the dynamical development of the non-equilibrium concentration fluctuations as a turbulent cascade process. Most crucially, the DFV theory predicts that the concentration fluctuations are non-Gaussian, with non-negligible higher-order cumulants. If these cumulants can be experimentally observed to be non-vanishing for large fluid domains, then such fluctuations do not arise as a “central limit theorem” in a hydrodynamical scaling limit and there is no sharp separation between the world of molecules and the macroscopic world.
(Università Sapienza, Roma)
Pairing rule and Lyapunov exponents for Euler-Ekmann incompressible flow with constant viscosity will be discussed and related to the equivalence conjectures with reversible flows.
(Università di Perugia)
We discuss minimum energy dissipation during digital computation, with reference both to computing and to memory storage, in the framework of nonlinear stochastic dynamics. The role of logical reversibility vs thermodynamical reversibility is critically reviewed.
(Niels Bohr Institute & University of Copenhagen)
When transcription factors in cells are controlled by negative feed back loops they possess a characteristic eigen frequency/period [1]. By applying an external oscillating signal it is possible to amplify the gene production when this period equals the external period. This gives rise to a genetic resonance phenomena. As the feed back loop often is non-linear we might obtain non-linear resonance with bi-stability and hysteresis. We present modeling and experimental results on the transcription factor p53 perturbed by oscillating nutlin signal with good agreement between theory and data. If cells are damaged by radiation leading to DNA damage, p53 will experience sustained oscillations. For p53 we show that phase transitions lead to condensates of repair proteins around damage sites which occur in an oscillating fashion thus preventing Oswald ripening [2]. The period of oscillations provides an optimal time scale for the repair mechanism.
[1] M.L. Heltberg, S. Krishna, L.P. Kadanoff and M.H. Jensen, "A tale of two rhythms: Locked
clocks and chaos in biology (Review)", Cell Systems, 12, 291-303 (2021).
[2] M.S. Heltberg, A. Lucchetti1, F.-S. Hsieh, D.P.M. Nguyen, S.-h.Chen and
Mogens H. Jensen, "Enhanced DNA repair through droplet formation and p53 oscillations",
Cell 185, 4394–4408 (2022).
(Università Sapienza, Roma)
To keep a system out of equilibrium for a long time requires a large amount of energy, infinite in the quasi static limit. This is a difficulty in developing a non—equilibrium thermodynamics. In this talk we will emphasise that in terms of suitable quantities a parallel can be established between reversible transformations in usual thermodynamics and quasi static transformations in dissipative diffusive systems considered by the macroscopic fluctuation theory.
(Università di Firenze)
In this talk we shall overview specific properties of the Discrete Nonlinear Schrodinger Equation concerning negative absolute temperature (NAT) states in equilibrium and in nonequilibrium conditions, which exhibit unexpected analogies with phenomena typical of quantum systems, like entaglement and quench into localized states.
(Università della Campania “Luigi Vanvitelli”, Napoli)
In this talk, I discuss various conceptual and technical challenges arising in the analysis of non-equilibrium systems, including the impact of coarse-graining and the problem of quantifying irreversibility from partial observations. Considering the paradigmatic case of a rotator immersed in a vibrofluidized granular gas, I firstly focus on Gaussian processes, demonstrating the impossibility of determining the thermodynamic state of a system from measurements of a single scalar. I then extend the discussion to linear processes evolving under Langevin equations driven by a mixture of Gaussian and Poissonian white noises, proving their lack of time-reversal symmetry. Interestingly, in these cases the absence of currents does not imply a vanishing entropy production. Finally, I introduce an empirical scale-dependent estimate for entropy production, to discuss the role of spatial and temporal resolutions in characterizing non-equilibrium features. In this way, I show that entropy production estimates are often inaccurate, requiring the exploration of alternative indicators of time-reversal symmetry breaking.
(Università dell'Insubria, Como)
Quantum dynamical entropies of the multiparticle Arnol'd cat
The multiparticle Arnol'd Cat is a non-phenomenological model of decoherence, constructed with the aim to develop a quantitative assessment of the complexity of quantum motion of an open system, in which the "environment" is treated exactly, in a sense.
In this talk I will start by reviewing the origin of this research in the problem of quantum chaos and of the classical limit of quantum mechanics. I will also mention early models of decoherence and their link to the former problem.
I will then show computer experiments confirming the validity of the abstract model under investigation, before introducing, computing, and discussing quantum dynamical entropies associated with its motion.
(Università di Camerino)
We study a repulsive thermal system governed by odd interactions. The interplay between oddness and inertia induces a non-equilibrium phase transition from a homogeneous to a non-homogeneous phase, characterized by bubbles induced by odd interactions. This phenomenon occurs in the absence of attractions and is generated by the competition between the standard pressure contribution due to particle repulsion and an effective surface tension generated by odd-induced centrifugal forces.
As a signature of the phase transition, the system exhibits vortex structures and oscillating spatial velocity correlations, which emerge close to the analytically predicted transition point. Our findings can be verified in granular experiments governed by odd interactions, such as spinners and colloidal magnets, and could be key to characterizing the emerging properties of metamaterials.
(Università di Torino, Italy)
Turbulence is by definition an out-of-equilibrium phenomenon, with energy flowing continuously from the large, input scales, to the small, dissipative ones. Temporal fluctuations in this energy flux produces corrections to the Kolmogorov energy spectrum which can be predicted using a multiscale perturbative approach. In this talk I will address this issue for a class of two-dimensional models known as α-turbulence, which includes the 2D Navier-Stokes equations and the Surface Quasi Geostrophic (SQG) model. I will discuss the theoretical prediction for the correction to the energy spectrum and I will compare it with the outcome of direct numerical simulations of the SQG model.
(Università Sapienza, Roma)
Emergent collective behaviour and complexity
I will discuss the general problem of studying the emergent collective behavior of an assembly of a large number of agents in the framework of statistical mechanics showing a few examples. I will discuss how complexity emerges in that framework.
I will present my viewpoints on complexity stressing the importance of multiple equilibria; I will then recall the genesis of the concept of multiple equilibria in natural sciences.
Finally, I will describe my contribution to the development of this concept in the framework of statistical mechanics and I will briefly mention the cornucopia of applications of these ideas both in physics and in other disciplines.
(Santa Marinella Research Institute)
The classic result by Kelly firmly established a clear quantitative connection between the amount of exchanged information and its value, at least for the case of gambling. Such a connection has been then extended to evolving populations, and, by the consideration of "demons", to stochastic thermodynamics. I shall present a short survey of the formulation of this connection and of the directions of present research.
(SISSA, Trieste)
The study of thermalization processes in isolated systems is of broad interest. It was pioneered by Fermi-Pasta-Ulam-Tsingou (FPUT), who discovered the “paradoxical” absence of thermalization in a one-dimensional lattice of coupled nonlinear oscillators. In this talk I will present a new avenue towards the understanding of thermalization, the presence of a power-law in the Fourier energy spectrum. A universal scaling exponent is obtained by mapping the FPUT model onto a pair of Burgers equations. Energy is transferred to higher Fourier modes like in “Burgers turbulence”, while a ``shock” develops on the lattice, and only at much longer times the system reaches energy equipartition.
(ENS-PSL, Paris)
Locking and parcellation in the cortical vascular dynamics
Oscillations in the diameter of blood vessels, a phenomenon known as vasomotion, are observed in pial arteries, at the surface of the brain. It is an active phenomenon, happening even in vitro; however, in vivo vasomotion is also locally phase-locked to oscillations in the underlying neuronal activity. This neurovascular coupling regulates the blood influx to the brain. Similar locking effects are also observed in the dynamics of peristaltic oscillations of the gut.
To understand those phenomena, we investigated a Ginzburg-Landau equation with a spatially varying natural frequency. We reproduced the observed phenomenology and identified space-time defects at the transition between two regions locked at different frequencies. Defects make phase models unsuitable. We determined the length of locked regions by simple analytical arguments, captured analytically the death of oscillations observed in a range of parameters, and explained the appearance of defects by a non-linear renormalization of the diffusivity, which turns negative and leads to instability.