LPTMC Seminars

Macroscopic fluctuations out of equilibrium

A system, subject to continuous exchanges of matter, energy or information with its surroundings, may reach a non-equilibrium steady state in which various currents break time-reversal invariance and continuously generate entropy. Such a state can not be accounted for by the Principles of Thermodynamics or the Gibbs-Boltzmann laws of statistical physics. Besides, linear response theory and the Onsager-Machlup functional provide useful descriptions of large scale fluctuations in such driven systems only at first order, in the vicinity of equilibrium.

In the last two decades, important advances in our understanding of processes far from equilibrium have been achieved, for which rare events, large deviations and fluctuations relations provide a unified framework. The emergence of universal features can be studied thanks to a variational principle, proposed by G. Jona-Lasinio and his collaborators, known as the Macroscopic Fluctuation Theory (MFT). In this theory, optimal fluctuations far from equilibrium are determined at a coarse-grained scale by two coupled non-linear hydrodynamic equations. The objective of this talk is to present these concepts and to illustrate them with some exact solutions of the MFT equations.

Slides (pdf)

Temporal Bell inequalities in a many-body system

Collective Monte Carlo updates through tensor network renormalization

We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present benchmarks for a variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass cases. With modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points. It compares well with other Monte Carlo schemes such as the Metropolis or Wolff algorithm: equilibration times appear to be reduced by a factor that varies between 40 and 2000, depending on the model and the observable being monitored. The scheme can be adapted to three dimensions, matrix models, or a confined gas of hard spheres.