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Navier-Stokes and equivalence conjectures
Giovanni Gallavotti
General considerations on the Equivalence conjectures and a review of few mathematical results.
Reversibility, Irreversibility, Friction and nonequilibrium ensembles in N-S equations
Giovanni Gallavotti
Viscosity, as a physical property of fluids, reflects an average effect over a chaotic microscopic motion described by Hamiltonian equations. It is proposed, as an example, that st…
Finite thermostats in classical and quantum nonequilibrium
Giovanni Gallavotti
Abstract: Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here a fo…
Viscosity, Reversibillity, Chaotic Hypothesis, Fluctuation Theorem and Lyapunov Pairing
Giovanni Gallavotti
Incompressible fluid equations are studied with UV cut-off and in periodic boundary conditions. Properties of the resulting ODEs holding uniformly in the cut-off are considered and…
Equivalent Ensembles, Turbulence and Fluctuation Theorem
Giovanni Gallavotti
Stationary states of Navier-Stokes fluids have been proposed to be described equivalently by several alternative equations, besides the NS equation itself. In particular equivalenc…
Nonequilibrium and Fluctuation Relation
Giovanni Gallavotti
A review on the fluctuation relation, fluctuation theorem and related topics.
Navier-Stokes equation: irreversibility turbulence and ensembles equivalence
Giovanni Gallavotti
The NS equation is considered (in 2 & 3 dimensions) with a fixed forcing on large scale; the stationary states form a family of probability distributions on the fluid velocity fiel…
Ergodicity: a historical perspective. Equilibrium and Nonequilibrium
Giovanni Gallavotti
A view on the physical meaning of the so called ergodic hypothesis: its role on the foundations of equilibrium statistical mechanics in mid '800, its interpretations and hints at i…
Kondo effect in the hierarchical s-d model
Giovanni Gallavotti, Ian Jauslin
The s-d model describes a chain of spin-1/2 electrons interacting magnetically with a two-level impurity. It was introduced to study the Kondo effect, in which the magnetic suscept…
Kondo effect in a fermionic hierarchical model
Giuseppe Benfatto, Giovanni Gallavotti, Ian Jauslin
In this paper, a fermionic hierarchical model is defined, inspired by the Kondo model, which describes a 1-dimensional lattice gas of spin-1/2 electrons interacting with a spin-1/2…
Renormalization group and divergences
Giovanni Gallavotti
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a…
Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model
Giovanni Gallavotti, Valerio Lucarini
We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in…
Nonequilibrium and irreversibility
Giovanni Gallavotti
The booklet contain an overview on selected recent developments in nonequilibrium statistical mechanics and chaos theory: SRB distributions, chaotic hypothesis, fluctuation theorem…
Nonequilibrium stationary state for a damped rotator
Giovanni Gallavotti, Alessandra Iacobucci, Stefano Olla
Perturbative construction of the nonequilibrium steady state of a rotator under a stochastic forcing while subject to torque and friction
Nonequilibrium, thermostats and thermodynamic limit
Giovanni Gallavotti, Errico Presutti
The relation between thermostats of "isoenergetic" and "frictionless" kind is studied and their equivalence in the thermodynamic limit is proved in space dimension and, for…
On Thermostats: Isokinetic or Hamiltonian? finite or infinite?
Giovanni Gallavotti
The relation between finite isokinetic thermostats and infinite Hamiltonian thermostats is studied and their equivalence is heuristically discussed.
Thermostats, chaos and Onsager reciprocity
Giovanni Gallavotti
Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the pha…
Fluctuation Theorem and Chaos
Giovanni Gallavotti
The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis…
Heat and Fluctuations from Order to Chaos
Giovanni Gallavotti
The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e.existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodi…
Quantum Nonequilibrium and Entropy creation
Giovanni Gallavotti
In sharp contrast to the corresponding classical systems cases it is not yet understood how to define a mechanical quantity with the interpretation of entropy creation rate for non…
Fluctuation relation, fluctuation theorem, thermostats and entropy creation in non equilibrium statistical Physics
Giovanni Gallavotti
A unified viewpoint is presented in margin to the ``Work, dissipation and fluctuations in nonequilibrium physics'', Bruxelles 22-25 March, 2006, where the topics were discussed by…
Microscopic chaos and macroscopic entropy in fluids
Giovanni Gallavotti
In nonequilibrium thermodynamics macroscopic entropy creation plays an important role. Here we study, from various viewpoints, its relation with the phase space contraction, which…
Boundary Dissipation in a Driven Hard Disk System
P. L. Garrido, G. Gallavotti
A simulation is performed aiming at checking the existence of a well defined stationary state for a two dimensional system of driven hard disks when energy dissipation takes place…
Entropy, Thermostats and Chaotic Hypothesis
Giovanni Gallavotti
The chaotic hypothesis is proposed as a basis for a general theory of nonequilibrium stationary states. Version 2: new comments added after presenting this talk at the Meeting ment…