Jorge Kurchan
Index: 1) Trajectories, distributions and path integrals. 2) Time-reversal and Equilibrium 3) Separation of timescales 4) Large Deviations 5) Metastability and dynamical phase transitions 6) Fluctuation Theorems and Jarzynski equality
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These notes are based on lectures given during the Summer School `Active matter and non-equilibrium statistical physics', held in Les Houches in September 2018. In these notes, we have merged our lectures into a single chapter broadly dedicated to `Non-equilibrium active systems'. We start with a discussion of generic features of non-equilibrium statistical mechanics, followed by a description of selected examples of the possible consequences of not being at thermal equilibrium. We then introduce the topic of dense glassy materials with a short review of glassy dynamics, rheology and jamming t…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second half, quantum systems. In Lecture 1, I briefly review the glass transition problem as a paradigm of slow relaxation and dynamical arrest in classical many-body systems. I discuss theoretical perspectives on how to think about glasses, and in particular how to model them in terms of kinetically constrained dynamics. In Lecture 2, I describe how via large deviat…
We review recent progress in developing effective field theories (EFTs) for non-equilibrium processes at finite temperature, including a new formulation of fluctuating hydrodynamics, and a new proof of the second law of thermodynamics. There are a number of new elements in formulating EFTs for such systems. Firstly, the nature of IR variables is very different from those of a system in equilibrium or near the vacuum. Secondly, while all static properties of an equilibrium system can in principle be extracted from the partition function, there appears no such quantity which can capture all non-…
Lectures on Statistical Mechanics
本文转录了 Allan N. Kaufman 教授 1972-1973 学年在 Berkeley 的研究生统计力学讲义，涵盖平衡态与非平衡态统计力学的核心主题。
Selected Topics of Social Physics: Equilibrium Systems
本文基于ETH Zurich课程，以教程兼综述形式介绍社会物理学平衡系统的基本定义、概念与典型模型，并呈现若干较新的原创模型。
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow to calculate the fluctuations and large deviations of the density and of the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example non-Gaussian fluctuations of density or non-convexity of the large deviation function which g…
The aim of these lectures, given at the Les Houches Summer School of Physics "Strongly Interacting Quantum Systems Out of Equilibrium", is providing an introduction to several important and interesting facets of out of equilibrium dynamics. In recent years, there has been a boost in the research on quantum systems out of equilibrium. If fifteen years ago hard condensed matter and classical statistical physics remained rather separate research fields, now the focus on several kinds of out of equilibrium dynamics is making them closer and closer. The aim of my lectures was to present to the stud…
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us with a unified description of many physical situations. These functions are expected to play, for systems far from equilibrium, a role akin to that of the thermodynamic potentials. These concepts will be illustrated by exact solutions of the Asymmetric Exclusion Process, a paradigm for non-equilibrium statistical physics.
Boulder Lectures on Thermal Dynamics and Hydrodynamic EFTs
本讲座介绍平衡与非平衡热化系统的有效场论构建，以“强到弱”自发对称破缺框架统一描述涨落流体动力学，并讨论输运参数的紫外/红外约束。
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of integrability based methods to problems in non-equilibrium statistical mechanics. The lectures were meant to complement this subject with background material on the equilibrium statistical mechanics of quantum spin chains from a vertex model perspective. The author was asked to provide a minimal introduction to quantum spin systems including notions like the redu…
The ideas of the constraint-based statistics are introduced. The axiom and six theorems of the constraint-based statistics are established.
Introduction to Langevin Stochastic Processes
本讲义介绍朗之万过程的性质与应用，内容汇编自ICTP赞助的多所学校、西湖大学PEBBLE夏令营及巴黎地区硕士课程的相关教学材料。
By suitable reformulations, we review the mathematical frameworks of six different approaches to the description of non-equilibrium dynamics with the purpose to set up a unified formulation of the Maximum Entropy Production (MEP) principle valid in all these contexts. In this way, we extend to such frameworks the concept of Steepest Entropy Ascent dynamics introduced by the present author in previous work on quantum thermodynamics. Actually, the present formulation constitutes a generalization also in the quantum thermodynamics framework. The analysis emphasizes that in the SEA-inspired implem…
In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences i…
Adding transitions to an equilibrium system increases the activity. Naively, one would expect this to hold also in out of equilibrium systems. This surprising effect is caused by adding heretofore forbidden transitions into less and less active states. We demonstrate, using relatively simple models, how adding transitions to an out of equilibrium system may in fact reduce the activity and even cause it to vanish. We investigate six related kinetically-constrained lattice gas models, some of which behave as naively expected while others exhibit this non-intuitive behavior. We introduce a semi-m…
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