## 16th Granada Seminar

### New Frontiers in **Nonequilibrium Statistical Physics**: from fundamentals, fluctuations, and hydrodynamics to biology and quantum nonequilibrium.

# SPEAKERS

16th Granada Seminar. Monday, June 14 at 6:00 pm Granada (Spain) time – 12:00 pm New York (USA) time

##### Informatic versus Thermodynamic Entropy Production in Active Systems

Stochastic thermodynamics connects the steady-state entropy production rate (EPR) of a system connected to a heat bath with the log ratio of probabilities of forward and time-reversed trajectories. Extending the resulting formula to coarse-grained models of systems much further from equilibrium, such as schools of fish or herds of wildebeest, results in an informatic EPR (IEPR) that depends only on order parameter dynamics and is no longer is connected with microscopic heat flow, but remains a valuable quantifier of macroscopic irreversibility. When the same coarse-grained models describe more microscopic processes (such as active phase separation within a biological cell), a connection to heat flow should be recoverable. To achieve this we can embed the coarse-grained model into a larger model involving explicit (if schematic) chemical reactions such that the whole system is governed by linear irreversible thermodynamics. All the active terms in the order parameter dynamics then become off-diagonal elements of an Onsager matrix whose symmetry determines the remaining chemical couplings and thus the full heat production. This exceeds the IEPR by a term that contains complementary spatial information to the IEPR itself.

16th Granada Seminar. Thursday, June 17 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### Long-range orientational order in 2D active matter

The birth of active matter physics may be traced back to 1995, when Tamas Vicsek and collaborators proposed to see collective motion as a spontaneously broken symmetry phase and introduced the now-famous Vicsek model. The same year, John Toner and Yuhai Tu, inspired by Vicsek, wrote down a field theory for this flying XY spin model, and obtained their landmark result: polar flocks can exhibit true long-range orientational order even in 2D.

I will first come back to these results and offer an updated view of such dry aligning dilute active matter (DADAM), where self-propelled point particles locally align their velocities in the presence of noise. I will then discuss some key facts and issues related to the various instances of long-range order presented by DADAM, including recent results showing that true long-range orientational order is also possible in 2D active nematics.

If time allows, I will discuss the robustness of the long-range ordered phases to various types of disorder.

16th Granada Seminar. Tuesday, June 8 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### Statistical measures for classical integrable systems

The pertinence of a statistical description of the long-term dynamics of a macroscopic system is not ensured in general, and much less so if the system is integrable. Great interest has been recently paid to check whether such an equilibrium-like approach could be useful to describe the temporal averages of well-chosen observables in the long term evolution of closed quantum systems. On the contrary, relatively little work has been devoted to the analysis of the same issue in the context of classical macroscopic integrable systems.

In this talk I will describe one particularly simple classical integrable interacting system, the so-called Neumann model, which can be related to the spherical Sherrington-Kirkpatrick (or p=2) model of disordered systems. With techniques of classical mechanics and disordered systems the Newtonian evolution after sudden quenches can be fully elucidated; in particular, in the long-times and large N limits. In parallel, a Generalized Gibbs Ensemble measure including all conserved charges can be used to evaluate statistical averages. The relevance of the latter approach can then be favourably put to the test for parameters in all sectors of the dynamic phase diagram, thus proving an extension of conventional statistical mechanics out of equilibrium.

16th Granada Seminar. Monday, June 7 at 6:00 pm Granada (Spain) time – 12:00 pm New York (USA) time

##### Renormalization and disorder: a simple toy model

The problem of the depinning transition of a line from a random substrate is one of the simplest problems in the the theory of disordered systems. It has a long history among physicists and mathematicians. Still there are some open questions about the nature of this transition.

After a brief review of our present understanding of the problem, I will discuss a simple tree-like toy model which indicates that, when disorder is relevant, the depinning transition becomes an infinite order transition of the Berezinski-Kosterlitz-Thouless type. I will also try to present some recent developments allowing to understand how the precise nature of the singularity at the transition depends on the distribution of disorder.

16th Granada Seminar. Thursday, June 10 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### Ecological Chaos and Microbial Diversity: What Should One Be Surprised By?

One of the discoveries enabled by the DNA sequencing revolution is the enormous diversity of microbes, extending down to the finest scales of genetic differences. Remarkably, extensive diversity within a single bacterial species can coexist in the same location and time. Traditional explanations in terms of a multitude of “niches” or of “ecological neutrality” are far from sufficient. And it is known that generalized Lotka-Volterra models of many interacting strains with no niche-like assumptions have no large stable communities. We show that a broad family of such models exhibit, instead, a highly-diverse spatio-temporally chaotic “phase” that is very robust. A partially exactly solvable model, a perfectly antisymmetric interaction matrix, provides the basis for a general analysis via dynamical mean-field theory. Potential applicability to host-pathogen systems, the conditions under which such a phase could evolve, and the degree of complexity of the interactions needed for it to occur will be discussed.

16th Granada Seminar. Monday, June 14 at 4:00 pm Granada (Spain) time – 10:00 am New York (USA) time

##### What can we compute, and what does it mean?

16th Granada Seminar. Tuesday, June 8 at 4:00 pm Granada (Spain) time – 10:00 pm New York (USA) time

##### Viscosity, reversibility, chaotic hypothesis in NS fluids

A statistical representation of viscosity in the framework of a thermodynamic formalism for the description of the stationary distributions of incompressible fluid flows. Various equations are proposed and their equivalence with the Navier-Stokes equations with cut-off N is presented as an instance of equivalence of ensembles. The cut-off N to infinity plays the role of the infinite volume limit, the viscosity the role of inverse temperature, the average enstrophy the role of the energy in thermodynamics,… In the infinite N limit the equivalence between the different descriptions is expected to be exact for the averages of large scale observables. Among the several equivalent equations some are reversible and therefore offer a different view of the viscosity in the context of the “Chaotic Hypothesis”.

16th Granada Seminar. Monday, June 14 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### Anomalous epidemic spreading

The actual Covid-19 epidemics has renewed interest in epidemic models and their coupling to economy and infrastructure. Here simple generalized SIS and SIR models are used to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on restrictions, as for instance the availability of healing resources that are generated by the healthy population. In this case one finds that an epidemic can spiral out of control into explosive spread, if the cost of recovery is above a critical cost. The onset of explosive epidemics exhibits a discontinuous transition under very general assumptions. Analytical expressions can be given for the critical cost and the size of the explosive jump in infection levels in terms the parameters that characterize the spreading process. The spread of an infection is also investigated when a system component can recover only if it remains reachable from a functioning central unit. More precisely, infection spreads from infected to healthy nodes, with the constraint that infected nodes only recover, if they remain connected to a pre-defined central node, through a path that contains only healthy nodes. This system converges to only one of two stationary states: either the whole population is healthy or it becomes completely infected. Simultaneous cluster infection can give rise to discontinuous jumps of different sizes in the number of failed nodes and local spread can abruptly turn uncontrollable, when it disrupts connectivity at a larger spatial scale. We introduce a general mathematical framework to describe and classify a variety of spreading dynamics. Interestingly, some scenarios turn out to exhibit spontaneous, unpredictable breakdown and recovery cascades. To foster the recovery of damaged or infected systems, we also propose a targeted recovery protocol where least- damaged or infected regions recover first. This can lead to spatial confinement of the infection within a well- defined radius. Finally, the model is adapted to the case of Covid-19 by taking into account the existence of asymptomatic cases, the detection of ill individuals through testing and the cost of testing and medical treatment. By introducing a lockdown period, we show that the final number of deaths can be reduced and find that there exists an optimal starting point for a lockdown.

16th Granada Seminar. Tuesday, June 15 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### Quantum thermalization and many-body localization: some fundamentals of quantum statistical mechanics

Most physical systems that contain many interacting degrees of freedom that are excited to energies well above of the ground state do act as a “bath” or “reservoir” for their own subsystems and thus go to thermal equilibrium under the system’s own dynamics, without any coupling to an external environment. This fundamental and long-studied process is called “thermalization”, and has been an active subject of recent research on quantum many-body systems, motivated by atomic, condensed matter, and high energy physics. One class of systems that fail to thermalize are systems that are many-body localized (MBL), which is the interacting version of Anderson localization. Such MBL systems instead remain localized near their initial state. There is a novel dynamic quantum phase transition between many-body localization and thermalization. I will give an overview of these topics.

16th Granada Seminar. Tuesday, June 8 at 6:00 pm Granada (Spain) time – 12:00 pm New York (USA) time

##### Features of nanoscale thermodynamics

In recent decades there has been increasing interest in applying the laws of thermodynamics to systems at very small length scales, such as biomolecules, optically manipulated colloidal particles, single electron devices, and trapped ions.

At these scales, new thermodynamic features emerge that are not present, or not relevant, in macroscopic thermodynamics. I will give an overview of theoretical and experimental progress that has been made in understanding these features.

I will focus in particular on the second law of thermodynamics, how it applies to nanoscale systems, and what we have learned about non-equilibrium fluctuations, “violations” of the second law, the thermodynamic arrow of time, nanoscale feedback control, and quantum thermodynamics.

16th Granada Seminar. Tuesday, June 15 at 3:00 pm Granada (Spain) time – 09:00 am New York (USA) time

##### Energy, momentum, and angular momentum transfers mediated by photons

Consider N objects in vacuum each locally may in thermal equilibrium but globally in nonequilibrium steady state. Transport of energy, momentum, or angular momentum is then possible mediated by the electromagnetic fields. It is useful to consider also an extra N+1 “object” which is the “bath-at-infinity”. Very general formulas of Meir-Wingreen type are derived based on the nonequilibrium Green’s functions for the photon field and the Keldysh formalism. The materials properties are represented by self energies. We illustrate the usefulness of the formulas and present some results of calculations, such as the angular momentum emission by a benzene ring driven by electric current, energy and angular momentum emission from a Haldane model of electrons, and also from graphene edges in nonequilibrium states.

16th Granada Seminar. Monday, June 7 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### On quasi-static transformations of diffusive systems, renormalized work and all that

For diffusive systems a theory of quasi static transformations of stationary states has been developed as a byproduct of the macroscopic fluctuation theory. In particular a notion of renormalized work has been introduced which in a quasi static transformation is equal to the variation of equilibrium free energy ΔF evaluated on these states. In addition a formula has been obtained relating ΔF to hydrodynamics. This formula implies the existence of an exact 1-form in the functional variables (E,λ), E the external field and λ the chemical potential, and introduces in a dissipative context an equivalence of transformations between fixed stationary states which recalls Clausius approach to entropy. Clausius formulated the second law of thermodynamics as a principle of equivalence of transformations and entropy provides the equivalence-value (Aequivalenzwerth) of a transformation.

16th Granada Seminar. Thursday, June 10 at 4:00 pm Granada (Spain) time – 10:00 am New York (USA) time

##### Competing species growing on a rugged front

When competing species expand into new territory, the population is dominated by descendants of a few successful ancestors at the expansion front. Successful ancestry is stochastic, but biased by fitness of the individual, as well as favorable geographic location. I will describe a simple model of range expansion of competing bacteria, in which reproduction and competition only take place at the growing front. Based on symmetry considerations a pair of nonlinear stochastic partial differential equations are constructed that describe the coevolution of the profile of the growing surface and the composition of the bacterial species on the front. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion will be presented.

16th Granada Seminar. Monday, June 7 at 4:00 pm Granada (Spain) time – 10:00 am New York (USA) time

##### Statistical Mechanical Ensembles and Typical Behavior of Macroscopic Systems

In this talk I will focus on describing, in a qualitative way, the reason statistical mechanics is able to predict, with great certainty, behavior of macroscopic systems, both in equilibrium and out of it.

I will relate this to the fact that this behaviour is typical for systems represented by the usual Gibbs ensembles or those derived from them. These take small phase space volume to indicate small probability.

I will not try to justify this here.

16th Granada Seminar. Friday, June 11 at 6:00 pm Granada (Spain) time – 12:00 pm New York (USA) time

##### Universal and Non-Universal Scaling in Brain Activity and Artificial Neural Networks

The human brain is in a (non-equilibrium) state of perpetual reverberating activity, even in the absence of stimuli and tasks. Shedding light onto the origin and functional meaning of such an activity has become essential to understand how the brain represents, processes and stores information, i.e. on “how it works”. An inspiring but controversial conjecture proposes that operating in the vicinity of a critical point, with its concomitant power-laws and scaling, (or, similarly, “at the edge of chaos”) could provide brain networks with key advantages for information processing and justify many of their empirically-observed dynamical features.

In this talk, I will very briefly summarise the “criticality hypothesis” focusing on the non-equilibrium Landau-Ginzburg field theory developed by our group. Then, I will present new results from a recently-proposed phenomenological renormalization group (RG) approach that allowed us to analyze actual data for the activity of thousands of individually recorded neurons. These analyses lead to a number of remarkable non-trivial features, such as the existence of non-Gaussian fixed-point probability distributions and a robust set of critical exponents, which is rather universal across brain regions. I will scrutinize these results under the light of a very recent theoretical approach, which imposses a necessary condition for the neural representation of visual inputs to be robust (continuous and differentiable) in terms of the properties of the neural activity (co)variance. This study allows us to distinguish between universal, noisy, background activity and non-universal, input-driven activity. Remarkably, the covariance matrix eigenspectrum in both types of activities decays as a power law much as in critical phenomena. Finally, I will discuss results in a type of artificial neural network trained to perform an image-classification task, in which optimal results and experimental-like power-law decaying eigenspectra are found when the network is set to operate “at the edge of chaos”.

16th Granada Seminar. Thursday, June 17 at 4:00 pm Granada (Spain) time – 10:00 am New York (USA) time

##### Hydrodynamics of integrable many-body systems

Integrable many-body systems can be characterised by having an extensive number of local conservation

laws. On the hydrodynamic scale (Euler), one thus expects to have a coupled system of a large number

of hyperbolic conservation laws. They have a very particular structure known as generalised hydrodynamics.

In my talk the classical Toda lattice will be used as an illustration.

16th Granada Seminar. Tuesday, June 15 at 4:00 pm Granada (Spain) time – 10:00 am New York (USA) time

##### Non-equilibrium interfaces

An interface is the moving or static boundary between two bulk phases. These can be free or constrained by the presence of a third phase, boundaries or inhomogeneities in the medium. At and near equilibrium the field has matured and has led to the prediction and observation of a range of novel non-trivial phenomena.

For non-equilibrium systems the situation is much less satisfactory, not least because distinct non-equilibrium systems do exist. Of these I will focus on interfaces of driven (passive) systems and active-passive interfaces.

In the former, general continuous stochastic growth equations, such as the KPZ, have proved useful also in the presence of surfaces or quenched disorder, capturing the long-range statistical properties of microscopic models and of the experiments.

Active matter is a much more recent field and work on active-passive interfaces has hardly begun. Concepts such as the surface tension of static interfaces are still open to debate. In addition, the nature of the bulk phases may be radically different (e.g. the existence of bubbly liquids in dry active matter and of active turbulence in wet nematics) raising fundamental questions on the effective descriptions that were so useful in driven passive systems.

In the first part of this talk I will review the non-equilibrium wetting phase diagram of driven passive systems based on effective interfacial models and illustrate how the rougheness of a driven interface may depend (somewhat surprisingly) on the anisotropy of the particle interactions, as suggested by experiments on drying droplets.

In the second part of the talk I will address active-passive interfaces. I will present results on interfaces of the hydrodynamic model of wet active nematics, which describe a range of observations made on propagating interfaces of bacterial films.

If time permits, I will discuss preliminary results on the wetting of scalar (dry) active matter and the roughness of its growing interface, based on massive simulations of a lattice model of active Brownian particles.

16th Granada Seminar. Friday, June 11 at 5:00 pm Granada (Spain) time – 11:00 am New York (USA) time

##### The scales of viral-host co-evolution

Living systems often attempt to calculate and predict the future state of the environment. Given the stochastic nature of many biological systems how is that possible? Does host-pathogen co-evolution constrain the space viral trajectories? I will show that co-evolution between immune systems and viruses in a finite-dimensional antigenic space can be described by an antigenic wave pushed forward and canalized by host-pathogen interactions. This leads to a new emergent timescale, the persistence time of the wave’s direction in antigenic space, which can be much longer than the coalescence time of the viral population. Since predicting the future state of a viral environment requires weighing the trust in new observations against prior experiences, I will present a view of the host immune system as a dynamic Bayesian machinery that updates its memory repertoire by balancing evidence from new pathogen encounters against past experience of infection to predict and prepare for future threats.

16th Granada Seminar. Thursday, June 17 at 6:00 pm Granada (Spain) time – 12:00 am New York (USA) time

##### Nonequilibirum Thermodynamics of Biochemical Circuits: Some Recent Results

A central problem in biology is how living systems manage to perform vital functions (e.g., replication, development, computing, etc.) accurately by using inherently stochastic biochemical circuits to process highly noisy information. What are the molecular mechanisms to control noise for accurate information processing? What is the energy cost for implementing these molecular mechanisms? In this talk, we will first present some of our recent work in addressing these two related general questions in the context of synchronization of molecular oscillators [1]. In the second part of the talk, we investigate the scaling behavior of the energy dissipation rate in biochemical networks. By developing a coarse-graining process in (chemical and physical) state space and a corresponding renormalization procedure for reaction rates, we find that energy dissipation rate has an inverse power-law dependence on the number of microscopic states in a coarse-grained state [2].

[1] “Nonequilibrium thermodynamics of coupled molecular oscillators: The energy cost and optimal design for synchronization”, D. Zhang, Y. Cao, Q. Ouyang, and Y. Tu, Nature Physics, 16, 95-100, 2020.

[2] “Scaling of Energy Dissipation in Nonequilibrium Reaction Networks”, Qiwei Yu, D. Zhang, and Y. Tu, Phys. Rev. Lett. (PRL),126, 080601, 2021.

16th Granada Seminar. Friday, June 11 at 4:00 pm Granada (Spain) time – 10:00 am New York (USA) time

##### Self-propelled Topological Defects

Active materials such as bacteria, molecular motors and eukaryotic cells continuously transform chemical energy taken from their surroundings to mechanical work. Dense active matter shows mesoscale turbulence, the emergence of chaotic flow structures characterised by high vorticity and self-propelled topological defects. I shall describe the physics of active defects, discussing active microfluidics, active disclinations and examples of topological defects in biological systems.