Latest Papers in Condensed Matter Physics

Statistical Mechanics

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Cumulative Merging Percolation and the epidemic transition of the Susceptible-Infected-Susceptible model in networks (1906.06300v1)

Claudio Castellano, Romualdo Pastor-Satorras

2019-06-14

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex networks, unveiling the existence of diverse mechanisms leading to the formation of a percolating cluster. The scaling solution accurately reproduces universal properties of the transition. This finding is used to infer the critical properties of the Susceptible-Infected-Susceptible (SIS) model for epidemics in infinite and finite power-law distributed networks, allowing us to rationalize and reconcile previously published results, thus ending a long-standing debate.

How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions (1808.07838v4)

Laura Tociu, Étienne Fodor, Takahiro Nemoto, Suriyanarayanan Vaikuntanathan

2018-08-23

The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials.

Generalization of the Wall Theorem to Out-of-equilibrium Conditions (1906.06264v1)

Ignacio Urrutia, Ivan Paganini, Claudio Pastorino

2019-06-14

The well-known Wall theorem states a simple and precise relation among temperature, pressure and density of a fluid at contact with a confining hard wall in thermodynamic equilibrium. In this Letter we develop an extension of the Wall theorem to out-of-equilibrium conditions, providing an exact relation between pressure, density and temperaure at the wall, valid for strong non-equilibrium situations. We derive analytically this Non-equilibrium Wall theorem for stationary states and validate it with non-equilibrium event-driven molecular-dynamics simulations. We compare the analytical expression with simulations by direct evaluation of temperature, density and pressure on the wall in linear regime, medium and very strong out-of-equilibrium conditions of a nanoconfined liquid under flow in stationary state, presenting viscous heating and heat transport. The agreement between theory and simulation is excellent, allowing for a conclusive validation. In addition, we explore the degree of accuracy of using the equilibrium Wall theorem and different expressions for the local temperature, employed in non-equilibrium molecular-dynamics simulations.

Kluitenberg-Verhás rheology of solids in the GENERIC framework (1812.07052v4)

Mátyás Szücs, Tamás Fülöp

2018-10-21

The internal variable methodology of nonequilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg-Verh'as model family [1]. This model family is distinguished not only from theoretical aspects but also on experimental grounds (see [2] for plastics and [3, 4, 5] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg-Verh'as model family can be presented in the nonequilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) [6, 7, 8, 9], for the benefit of both thermodynamical methodologies as well as for promising practical applications.

The committee machine: Computational to statistical gaps in learning a two-layers neural network (1806.05451v2)

Benjamin Aubin, Antoine Maillard, Jean Barbier, Florent Krzakala, Nicolas Macris, Lenka Zdeborová

2018-06-14

Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this contribution, we provide a rigorous justification of these approaches for a two-layers neural network model called the committee machine. We also introduce a version of the approximate message passing (AMP) algorithm for the committee machine that allows to perform optimal learning in polynomial time for a large set of parameters. We find that there are regimes in which a low generalization error is information-theoretically achievable while the AMP algorithm fails to deliver it, strongly suggesting that no efficient algorithm exists for those cases, and unveiling a large computational gap.

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