Recent Advances in Percolation Theory
Hans J. Herrmann
PMMH, ESPCI Paris, France and UFC, Fortaleza, Brazil
In the course we will first introduce the basic concepts of percolation, its scaling laws and its fractal subsets like the backbone, the elastic backbone, the shortest path with its perturbations and the distribution of currents. We will also present rigidity percolation, bootstrap percolation and drilling percolation. Particular emphasis will be given to discontinuous percolation like explosive and bridge percolation as well as abrupt epidemic spreading. Next, we will consider correlated surfaces with Hurst exponents to study the fractality of its coastlines, its watersheds and its retention capacity. We will investigate the Schramm-Loewner Evolution of various loop-less curves on top of these surfaces. We will dedicate the end of the course to failure models, like the fuse model, metallic breakdown and the optimal path crack.
Control Theory and Stochastic Thermodynamics
John Bechhoefer
Simon Fraser University
Canada
Control theory is an important topic for physicists that rarely is covered by standard curricula. In these three sessions, I will introduce the main ideas and discuss basic ideas such as feedback, feedforward, and robustness and how they apply to stochastic thermodynamics.
- Session 1 will introduce control theory as a whole and motivate its interest and value to physicists, both for practical reasons (e.g. improving experiments, e.g. via PID feedback) and theoretical reasons (e.g. its connections with information theory and thermodynamics).
- Session 2 will focus on optimal control, including Hamiltonian methods and Pontryagin’s principle, and discuss its application to stochastic systems.
- Session 3 will focus on state estimation, including Bayesian and Kalman filters, and show that many practical problems in the treatment of experiment have in common the need to infer “hidden” dynamical states from a sequence of measurements.
Quantum thermodynamics: fluctuations and thermal machines
Gonzalo Manzano
Instituto de Física Interdisciplinar y Sistemas Complejos - IFISC (CSIC-UIB)
Spain
In the last decades thermodynamics have been extended to small (microscopic or nanoscopic) scales, where fluctuations play a major role pushing systems out of equilibrium, and where genuine quantum effects cannot be neglected anymore. Quantum thermodynamics is an interdisciplinary and growing field that places at the intersection of quantum information and non-equilibrium statistical physics. It aims to study quantum systems from a new perspective, emphasizing the energetic and entropic costs of quantum operations, and investigating possible enhancements of classical thermodynamic tasks by means of genuine quantum effects.
In this mini-course I will introduce some of the main concepts in quantum thermodynamics, including the definitions of work, heat or entropy production at the quantum level, but also some of their applications, such as designing quantum thermal machines that perform useful thermodynamic tasks. For that purpose I will introduce some basics of open and monitored quantum systems, that will allow us to describe fluctuations of relevant thermodynamic quantities in generic quantum processes. Using these tools we will also see how to derive universal results such as the so-called fluctuation theorems, as well as other related inequalities, altogether refining our understanding of the second law and irreversibility.
