## 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

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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

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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

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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

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

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

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

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

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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

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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.