Session U7: Teaching Nonequilibrium Statistical Mechanics for the Needs of 21st Century Physicists

Nonequilibrium Statistical Mechanics for Today's Graduate Students

The notion of nonequilibrium statistical mechanics as a tool for analysis of many body systems is emphasized to support its value to graduate students in general. Its evolution across a wide range of fields within and beyond physics over the past half century is recalled. Much of the earlier focus on detailed and systematic applications to simple systems has been replaced by more qualitative analysis of complex systems. A case is made for the utility of a carefully composed course in nonequilibrium statistical mechanics as a means of thinking about problems in condensed matter physics, materials sciences, chemical physics, and particle physics.   

Entropy, Order Parameters, and Complexity: Incorporating the last 50 years into the statistical mechanics curriculum

The purview of statistical mechanics has grown rapidly in the past decades, with nonequilibrium extensions and applications to dynamical systems, molecular biology and bioinformatics, complex systems and networks, digital communication and information theory, and econophysics and other social sciences. It is our responsibility to join these new insights to the old wisdom in the field, and to distill the key ideas for the next generation. We should include (a) Shannon entropy, data compression, and reversible computation, (b) chaotic motion, ergodicity and the KAM theorem, and renormalization-group treatments of the onset of chaos, (c) molecular motors and hidden Markov models for analyzing genomic data. We should make statistical mechanics useful and comprehensible to those outside of physics, eschewing applications (Clausius-Clapeyron equations, $c_{p}$ vs. $c_{v})$ and methods (quantum mechanics) accessible and interesting only to condensed-matter physicists and physical chemists. See \textit{Entropy, Order Parameters, and Complexity} (http://www.physics.cornell.edu/sethna/StatMech/), OUP, 2006.   

Teaching at the edge of knowledge: Non-equilibrium statistical physics

As physicists become increasingly interested in biological problems, we frequently find ourselves confronted with complex open systems, involving many interacting constituents and characterized by non-vanishing fluxes of mass or energy. Faced with the task of predicting macroscopic behaviors from microscopic information for these non-equilibrium systems, the familiar Gibbs-Boltzmann framework fails. The development of a comprehensive theoretical characterization of non-equilibrium behavior is one of the key challenges of modern condensed matter physics. In its absence, several approaches have been developed, from master equations to thermostatted molecular dynamics, which provide key insights into the rich and often surprising phenomenology of systems far from equilibrium. \newline In my talk, I will address some of these methods, selecting those that are most relevant for a broad range of interdisciplinary problems from biology to traffic, finance, and sociology. The ``portability'' of these methods makes them valuable for graduate students from a variety of disciplines. To illustrate how different methods can complement each other when probing a problem from, e.g., the life sciences, I will discuss some recent attempts at modeling translation, i.e., the process by which the genetic information encoded on an mRNA is translated into the corresponding protein.   

Non-equilibrium statistical mechanics in the context of biological physics

Living systems are inherently out of equilibrium and operate in a fluctuating environment. The current challenges and interests in quantitative biology thus provide a great opportunity to introduce and develop methods from non-equilibrium statistical physics. For example, Master equations for evolution of probability find applications in mutating sequences, molecular motors, and signaling networks.   

The Onsager Matrix Reloaded: Teaching Nonequilibrium Statistical Mechanics via Modern Applications

Traditional texts and courses on nonequilibrium statistical mechanics (NESM) focus on fundamentals and outmoded examples that do not reflect the explosion of applications and developments from recent decades. With the burgeoning interest in multidisciplinary approaches to key problems in science and technology, in which physics and quantitative methods play a central role, NESM emerges as one of the unifying and pivotal techniques that physicists have to offer. I outline an approach to teaching NESM that emphasizes less formal theory and more modern applications, centered around developments in (e.g.) pattern formation, materials science, biology, fluid dynamics and atmospheric science.