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Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
We propose a mathematical derivation of stochastic compressible Navier-Stokes equation. We consider many-particle systems with a Hamiltonian dynamics supplemented by a friction term and environmental noise. Both the interaction potential…
Most existing works on transportation dynamics focus on networks of a fixed structure, but networks whose nodes are mobile have become widespread, such as cell-phone networks. We introduce a model to explore the basic physics of…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting…
Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…
A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…
In this review paper we aim at illustrating recent achievements in anomalous heat diffusion, while highlighting open problems and research perspectives. We briefly recall the main features of the phenomenon for low-dimensional classical…
A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the…
We apply a recently proposed novel thermostating mechanism to an interacting many-particle system where the bulk particles are moving according to Hamiltonian dynamics. At the boundaries the system is thermalized by deterministic and…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws, that can be derived from experimental data averaged in time or space,assuming the system in a steady state. One of the major…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent…
The thermal conductivity of classical multi-component fluids is seemingly affected by the intrinsic arbitrariness in the definition of the atomic energies and it is ill-conditioned numerically, when evaluated from the Green-Kubo theory of…
Energy transfer in small nanosized systems can be very different from that in their macroscopic counterparts due to reduced dimensionality, interaction with surfaces, disorder, and large fluctuations. Those ingredients may induce…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
This survey describes the recent advances in the construction of Markov partitions for nonuniformly hyperbolic systems. One important feature of this development comes from a finer theory of nonuniformly hyperbolic systems, which we also…
Scaling laws for the transport and heating of trace heavy ions in low-frequency, magnetized plasma turbulence are derived and compared with direct numerical simulations. The predicted dependences of turbulent fluxes and heating on ion…
Experiments show that macroscopic systems in a stationary nonequilibrium state exhibit long range correlations of the local thermodynamic variables. In previous papers we proposed a Hamilton-Jacobi equation for the nonequilibrium free…