The Erwin, Schrödinger International Boltzmanngasse, Giovanni Gallavotti, Fabio Perroni, Giovanni Gallavotti, Fabio Perroni
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Nonequilibrium, thermostats and thermodynamic limit (2009)
Gallavotti, Giovanni, Presutti, Errico
The relation between thermostats of "isoenergetic" and "frictionless" kind is studied and their equivalence in the thermodynamic limit is proved in space dimension $d=1,2$ and, for special...
of the Perturbations in Classical Mechanics and Invariance of the Frequency Spectrum (2008)
Abstract. We introduce an analogue to the renormalization theory (of quantum fields) into classical mechanics. We also find an integrability criterion guaranteeing the convergence of Birkhoff s...
16th International Congress on Mathematical Physics (2008)
Aizenman, Michael, Daubechies, Ingrid, Exner, Pavel, Froehlich, Juerg, Gallavotti, Giovanni, Sinai, Yakov, ...
On Thermostats: Isokinetic or Hamiltonian? finite or infinite? (2008)
The relation between finite isokinetic thermostats and infinite Hamiltonian thermostats is studied and their equivalence is heuristically discussed.
Thermostats, chaos and Onsager reciprocity (2008)
Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space...
Chaotic hypothesis From Scholarpedia (2008)
Chaotic Hypothesis: assumes that quite generally a system exhibiting chaotic motions does so in a maximal form so that it can be supposed to be a transitive hyperbolic system. This is analogous to...
Fluctuation Theorem and Chaos (2008)
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. In nonequilibrium...
Numerical Methods and Results in the FPU Problem (2008)
PALEARI, SIMONE, PENATI, TIZIANO, Simone Paleari, Tiziano Penati, Giovanni Gallavotti
Numerical Methods and Results in the FPU Problem / Simone Paleari, Tiziano Penati. - (Lecture Notes in Physics ; 728). - In: The Fermi-Pasta-Ulam Problem : a Status Report ; [a cura di] Giovanni...
Heat and Fluctuations from Order to Chaos (2008)
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 Ergodic Hypothesis, valid...
Fluctuation Theorem and Chaos (2008)
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. In nonequilibrium...
: Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the...
Giovanni Gallavotti, Lamberto Rondoni, Enrico Segre
Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics
x1. The Luttinger model. (2007)
Abstract: The Luttinger model was introduced to illustrate the possibility of a perturbative treatment of the singularity at the Fermi surface, already known to be \anomalous " from the...
Heat and Fluctuations from Order to Chaos (2007)
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 Ergodic Hypothesis, valid...
Quantum Nonequilibrium and Entropy creation (2007)
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 nonequilibrum...
Heat and Fluctuations from Order to Chaos (2007)
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 Ergodic Hypothesis, valid...
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 various authors and...
Microscopic chaos and macroscopic entropy in fluids (2006)
In nonequilibrium thermodynamics macroscopic entropy creation plays an important role. Here we study, from various viewpoints, its relation with the phase space contraction, which has been recently...
Entropy, Thermostats and Chaotic Hypothesis (2006)
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 mentioned in the...
Entropy, Nonequilibrium, Chaos and Infinitesimals (2006)
A survey of the approach to Statistical Mechanics following Boltzmann's theory of ensembles and ergodic hypothesis leading to chaoticity as a unifying principle of equilibrium and nonequilibrium...
Constructive Quantum Field Theory (2005)
A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.
Stationary nonequilibrium statistical mechanics (2005)
A brief review on the dynamical systems approach to nonequilibrium statistical mechanics and chaotic dynamics
Fractional Lindstedt series (2005)
Gallavotti, Giovanni, Gentile, Guido, Giuliani, Alessandro
The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter,...
Equilibrium Statistical Mechanics (2005)
An introductory review of Classical Statistical Mechanics
An overview of the foundations of Classical Mechanics
CKN theory of singularities of weak solutions of the Navier-Stokes equations (2005)
The lectures are devoted to a complete exposition of the theory of singularities of the Navier Stokes equations solution studied by Leray, in a simple geometrical setting in which the fluid is...
Fluctuation theorem revisited (2004)
Recently the ``Fluctuation theorem'' has been criticized and incorrect incorrect contents have been atributed to it. Here I reestablish and comment the original statements.
The various versions of cond-mat/0312353 discuss results obtained by me&coworkers in the last decade. I have received requests to comment on the paper and the comments are collected here, including...
Entropy production in nonequilibrium thermodynamics: a review (2003)
Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in...
Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics (2002)
Gallavotti, Giovanni, Rondoni, Lamberto, Segre, Enrico
We perform numerical experiments to study the Lyapunov spectra of dynamical systems associated with the Navier--Stokes (NS) equation in two spatial dimensions truncated over the Fourier basis....
The Luttinger model: its role in the RG-theory of one dimensional many body Fermi systems (2000)
The Luttinger model was introduced to illustrate the theory of Tomonaga via an exactly soluble model. It became soon the subject of great interest also on the part of Mathematical Physics and a key...
Entropy driven intermitency (2000)
This note reviews some physical aspects of the chaotic hypothesis in nonequilibrium statistical mechanics and attempts at the physical interpretation of the fluctuation theorem as a quantitative...
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of...
We present a review of the chaotic hypothesis and discuss its applications to intermittency in statistical mechanics and fluid mechanics proposing a quantitative definition. Entropy creation rate is...
Fluctuations and entropy driven space-time intermittency in Navier-Stokes fluids (2000)
We analyze the physical meaning of fluctuations of the phase space contraction rate, that we also call entropy creation rate, and its observability in space-time intermittency phenomena. For...
Gallavotti, Giovanni, Perroni, Fabio
An experimental test of a large fluctuation theorem is performed on a chain of coupled ``cat maps''. Our interest is focused on the behavior of a subsystem of this chain. A local entropy creation...
Quasi periodic motions from Hipparchus to Kolmogorov (1999)
The evolution of the conception of motion as composed by circular uniform motions is analyzed, stressing its continuity from antiquity to our days.
The ergodic hypothesis outgrew from the ancient conception of motion as periodic or quasi periodic. It did cause a revision of our views of motion, particularly through Boltzmann and Poincar\'e: we...
Lindstedt series and Kolmogorov theorem. (1999)
: the KAM theorem from a combinatorial viewpoint. Lindstedt, Newcomb and Poincar'e introduced a remarkable trigonometric series motivated by the analysis of the three body problem, [P]. In...
Giovanni Gallavotti, Fabio Perroni
An experimental test of a large uctuation theorem is performed on a chain of coupled \cat maps". Our interest is focused on the behavior of a subsystem of this chain. A local entropy creation...
Giovanni Gallavotti, A. Moro Roma
Abstract. the KAM theorem from a combinatorial viewpoint. Lindstedt, Newcomb and Poincar'e introduced a remarkable trigonometric series motivated by the analysis of the three body problem, [1]....
Chaotic Hypothesis and Universal Large Deviations Properties (1998)
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by...
A local fluctuation theorem (1998)
A mechanism for the validity of a local version of the fluctuation theorem, uniform in the system size, is discussed for a reversible chain of weakly coupled Anosov systems.
Reminiscences on science at I.H.E.S. A problem on homoclinic theory and a brief review (1998)
On the occasion of the 40-th anniversary of IHES I present a few scientific reminiscences: most of my scientific life has been marked by my visits and I run through them concluding with the analysis...
Gallavotti, Giovanni, Gentile, Guido, Mastropietro, Vieri
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time...
Lindstedt series, ultraviolet divergences and Moser's theorem (1998)
Bonetto, Federico, Gallavotti, Giovanni, Gentile, Guido, Mastropietro, Vieri
A local fluctuation theorem (1998)
a simple consequence of a time reversal symmetry; it deals with motions which are chaotic in the strong mathematical sense of being hyperbolic and transitive (ie are generated by smooth hyperbolic...
Chaotic dynamics, fluctuations, nonequilibrium ensembles (1997)
A review of some recent results and ideas about the expected behaviour of large chaotic systems and fluids.
Local integrability of hyperbolic oscillators is discussed to provide an introductory example of the Arnold's diffusion phenomenon in a forced pendulum. This is a text prepared for the the ISI summer...
Fast Arnold's diffusion in isochronous systems (1997)
We provide an illustration of a mechanism for Arnold's diffusion following a nonvariational approach and find explicit estimates for the diffusion time.
Fluctuation Patterns and Conditional Reversibility in Nonequilibrium Systems (1997)
: Fluctuations of observables as functions of time, or fluctuation patterns, are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary...
Quasi linear flows on tori: regularity of their linearization (1996)
Bonetto, Federico, Gallavotti, Giovanni, Gentile, Guido, Mastropietro, Vieri
Under suitable conditions a flow on a torus $C^{(p)}$--close, with $p$ large enough, to a quasi periodic diophantine rotation is shown to be conjugated to the quasi periodic rotation by a map that is...
Dynamical ensembles equivalence in fluid mechanics (1996)
Dissipative Euler and Navier Stokes equations are discussed with the aim of proposing several experiments apt to test the equivalence of dynamical ensembles and the chaotic hypothesis.
Equivalence of dynamical ensembles and Navier Stokes equations (1996)
A reversible version of the Navier Stokes equation is studied. A conjecture emerges stating the equivalence between the reversible equation and the usual Navier Stokes equation. The latter appears as...
The fluctuation theorem (FT), the first derived consequence of the {\it Chaotic Hypothesis} (CH) of ref. [GC1], can be considered as an extension to arbitrary forcing fields of the fluctuation...
Methods in the Theory of Quasi Periodic Motions (1996)
Giovanni Gallavotti, V. Mastropietro
. Recent results on the theory of the Hamilton--Jacobi equation and the regularity of their solutions, in spite of the non regularity of the data, are reviewed, and discussed with attention to the...
Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem (1995)
It is shown that the "chaoticity hypothesis", analogous to Ruelle's principle for turbulence and recently introduced in statistical mechanics, implies the Onsager reciprocity and the fluctuation...
Chaotic principle: some applications to developed turbulence (1995)
Some models for developed turbulence are considered; they are shown to obey a large fluctuations theorem, and one among them also obeys a response reciprocity relation of Onsager's type. This...
Lindstedt series and Kolmogorov theorem (1995)
The KAM theorem from a combinatorial viewpoint.
Reversible Anosov diffeomorphisms and large deviations (1995)
The volume contraction obeys a large deviation rule.
Entropia e Informazione. (1995)
: The Boltzmann limit conjecture of Grad is discussed in general and proved for the Lorentz gas case(where the Boltzmann equation is linear). This is a reprint of an unpublished preprint of 1972,...
Lindstedt series and Kolmogorov theorem. (1995)
: the KAM theorem from a combinatorial viewpoint. Lindstedt, Newcomb and Poincar'e introduced a remarkable trigonometric series motivated by the analysis of the three body problem, [P]. In...
The seed ye sow, another reaps x1 Mathematical Physics, in general. It is quite difficult to find a subject to discuss as afterthought about a conference on Mathematical Physics towards the XXI...
Hamilton formalization of classical mechanics. The latter made available to everybody the possibility of computing in an unambigous way the solution to mechanics problems which were accessible only...
Billiards Correlation Functions (1994)
Pedro L. Garrido, Giovanni Gallavotti
: We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing...
: A selfcontained proof of the KAM theorem in the Thirring model is discussed. Keywords: KAM, invariant tori, classical mechanics, perturbation theory, chaos I shall particularize the Eliasson...
Non recursive proof of the KAM theorem (1993)
Gallavotti, Giovanni, Gentile, Guido
A selfcontained proof of the KAM theorem in the Thirring model is discussed, completely relaxing the ``strong diophantine property'' hypothesis used in previous papers. Keywords: \it KAM, invariant...
A selfcontained proof of the KAM theorem in the Thirring model is discussed.
Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the...
Stability of motions near resonances in quasi-integrable Hamiltonian systems (1986)
Giancarlo Benettin, Giovanni Gallavotti
Nekhoroshev's theorem on the stability of motions in quasi-integrable Hamiltonian systems is revisited. At variance with the proofs already available in the literature, we explicitly consider...
G.: Perturbation theory and non renormalizable scalar fields (1986)
Giovanni Felder, Giovanni Gallavotti
Abstract. We study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of: P(φ) : d when one does not allow any...
Stability and equilibrium states of infinite classical systems (1976)
Aizenman, Michael, Gallavotti, Giovanni, Goldstein, Sheldon, Lebowitz, Joel L.
© by Springer-Verlag 1974 Billiards and Bernoulli Schemes (1974)
Giovanni Gallavotti, Donald S. Ornstein
Abstract. Some two dimensional billiards are Bernoulli flows. "Billiards " will mean a point particle moving on a table with smooth convex obstacles and bouncing elastically against...
Markov processes, Bernoulli schemes, and Ising (1973)
Francesco Di Liberto, Giovanni Gallavotti, Lucio Russo
Abstract. We give conditions for the Bernoullicity of the v-dimensional Markov processes. 1. Symbols and Definitions Z v is the v-dimensional lattice of the points with integral coordinates and K = I...
The phase separation line in the two--dimensional Ising model (1972)
Abstract. We prove that, at low temperature, the line of separation between the two pure phases shows large fluctuations in shape. This implies the translation invariance of the correlation functions...
Rigorous Theory Of The Boltzmann Equation In The Lorentz Gas (1972)
Giovanni Gallavotti, Istituto Di Fisica, Analisi Funzionale
: The Boltzmann limit conjecture of Grad is discussed in general and proved for the Lorentz gas case (where the Boltzmann equation is linear). This is a reprint of an unpublished preprint of 1972,...
Non recursive proof of the KAM theorem
Giovanni Gallavotti, Guido Gentile
: A selfcontained proof of the KAM theorem in the Thirring model is discussed, completely relaxing the "strong diophantine property" hypothesis used in previous papers. Keywords: KAM,...