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We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…

Statistical Mechanics · Physics 2009-11-13 Stefano Ruffo

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…

Statistical Mechanics · Physics 2017-03-29 Uwe C. Täuber

We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…

Statistical Mechanics · Physics 2025-07-29 Marco Cattaneo , Marco Baldovin , Dario Lucente , Paolo Muratore-Ginanneschi , Angelo Vulpiani

We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to…

Quantum Physics · Physics 2012-11-27 A. Smirne , E. -M. Laine , H. -P. Breuer , J. Piilo , B. Vacchini

Based on the 2PI quantum effective action of the linear sigma model with constituent quarks, we develop a transport approach to study systems out of equilibrium. In particular, we focus on the chiral phase transition as well as the critical…

High Energy Physics - Phenomenology · Physics 2015-06-18 Alex Meistrenko , Christian Wesp , Hendrik van Hees , Carsten Greiner

In the present note, we discuss a simple example of a macroscopic quantum many-body system in which the approach to thermal equilibrium from an arbitrary initial state in the microcanonical energy shell is proved without relying on any…

Statistical Mechanics · Physics 2024-04-09 Hal Tasaki

The fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here prove that in a macroscopic quantum system for a…

Statistical Mechanics · Physics 2015-06-18 Sheldon Goldstein , Takashi Hara , Hal Tasaki

Isotropization occurs on time scales much shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in complex many body…

High Energy Physics - Phenomenology · Physics 2010-11-05 J. Berges , Sz. Borsanyi , C. Wetterich

To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. Despite the fact that the theory is more than 100 years old, we are still discussing its foundations…

Quantum Physics · Physics 2017-03-14 Fabio Anza , Vlatko Vedral

In this brief review we introduce the methods of quantum field theory out of equilibrium and study the non-equilibrium aspects of phase transitions. Specifically we critically study the picture of the ``slow-roll'' phase transition in the…

High Energy Physics - Theory · Physics 2009-09-25 D. Boyanovsky , H. J. de Vega , R. Holman

We investigate the thermalization and the chemical equilibration of a parton plasma created from Au+Au collision at LHC and RHIC energies starting from the early moment when the particle momentum distributions in the central region become…

High Energy Physics - Phenomenology · Physics 2008-11-26 S. M. H. Wong

The quark-gluon plasma created in heavy-ion collisions is not in local thermal equilibrium at early times. Despite this, dissipative hydrodynamics describes the evolution of the energy-momentum tensor quite well after only roughly 0.5 - 1…

High Energy Physics - Phenomenology · Physics 2019-07-24 Michael Strickland

An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the chain particles have random displacements and random velocities corresponding to a…

Statistical Mechanics · Physics 2020-11-04 Anton M. Krivtsov , Andrey S. Murachev

Thermalization play a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter.…

Strongly Correlated Electrons · Physics 2015-03-17 Didier Poilblanc

We investigate the early time dynamics of heavy ion collisions studying the time evolution of the energy-momentum tensor as well as energy-momentum correlations within a uniformly thermalizing holographic QGP. From these quantities, we…

An important question in heavy-ion collisions is how the initial far-from-equilibrium medium evolves and thermalizes while it undergoes a rapid longitudinal expansion. In this presentation, we show how to use the two-particle irreducible…

Nuclear Theory · Physics 2025-09-23 Francois Gelis

We study thermal equilibration after preheating in inflationary cosmology, which is an important step towards a comprehensive understanding of cosmic thermal history. By noticing that the problem is parallel to thermalization after a…

High Energy Physics - Phenomenology · Physics 2019-08-28 Robert Brandenberger , Ryo Namba , Rudnei O. Ramos

We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems, with Hamiltonians of the form $\hat{H}_0+g\hat{V}$, where $\hat{H}_0$ is nonintegrable and $g\hat{V}$ is a…

Statistical Mechanics · Physics 2021-11-19 Krishnanand Mallayya , Marcos Rigol

We consider quenches of a quantum system that is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. Technically, our main result is a systematic expansion of the…

Statistical Mechanics · Physics 2025-11-14 Lennart Dabelow

We investigate the relaxational dynamics of the order parameter of chiral symmetry breaking, the sigma mean-field, with a heat bath consisting of quarks and antiquarks. A semiclassical stochastic Langevin equation of motion is obtained from…

Nuclear Theory · Physics 2015-05-28 Marlene Nahrgang , Stefan Leupold , Marcus Bleicher