This award supports theoretical research and education in a continuing effort to understand the complex behavior in interacting many-particle systems driven far from thermal equilibrium. Unlike their equilibrium counterparts, these systems "both physical and biological" cannot be described by the well established framework of Boltzmann and Gibbs. One essential difference is that these systems are in contact with more than one reservoir in such a way that nontrivial fluxes through the systems persist, even when they are in time-independent states. Good examples include all living organisms, the earth as an ecosystem, and many aspects of our modern infrastructure. The key challenge is to devise a reliable theoretical framework which predicts macroscopic observables from the underlying microscopic dynamics.
An overarching framework for non-equilibrium statistical mechanics is lacking. The PIs will study the least complex models which include essential characteristics of far-from-equilibrium physics. The PIs will focus on models with the potential for applications to biological systems. The totally asymmetric simple exclusion process will be a focus of study. Many properties of the original model are known analytically. However, generalizations of the model become the building blocks for a quantitative approach to modeling protein production in a cell. Progress in this field will contribute to understanding biological transport processes, inspire possible ways to design and synthesize proteins, as well as to valuable insights for addressing fundamental issues in non-equilibrium statistical physics, such as the role of non-trivial probability current loops in configuration space.
Given the range of topics and methods in this research, it lends itself readily to the education of young scientists at virtually all levels. In this way, this award contributes to the training of the next generation of a globally competitive workforce.
NONTECHNICAL SUMMARY This award supports theoretical research and education in statistical physics of systems driven far from equilibrium. Living things provide an important example of a system composed of many particles or parts that is far from the balanced state known as equilibrium. The main goal of this research is to elucidate the foundations of a theoretical and conceptual framework for materials and other systems that are far from equilibrium. The PIs seek an overarching principle which generalizes the extremely successful fundamental hypothesis of the field of equilibrium statistical mechanics. This research covers a wide range of topics and exploits a variety of methods: from the simplest mathematical models to models of complex living systems and from readily accessible computer simulations to sophisticated field theoretic techniques. A central focus of this research lies at the interface of biology and materials research. The PIs will study protein production by messenger RNA in cells. It will be modeled as an assembly-line-like activity and studied with both simulations and powerful tools in mathematics and statistics. This research will apply the insights gained to investigate a wider range of transport systems, from traffic flow to information on the Internet.
Given the range of topics and methods in this research, it lends itself readily to the education of young scientists at virtually all levels. In this way, this award contributes to the training of the next generation of a globally competitive workforce.
The unifying theme of this project is the characterization and understanding of complex behavior of a variety of systems in nature when driven far from equilibrium. Examples of such system include all living organisms, our ecosystem, as well as many physical systems from the nano- to the astronomical scales. Unlike system in equilibrium, these cannot exist as soon as we deprive them from a constant through-flux of energy or matter. The key challenge is to devise a reliable theoretical framework which predicts the rich range of phenomena at the macroscopic level (e.g., life forms, climate) from the simple constituents and underlying dynamics at the microscopic level (e.g., atoms, molecules, and laws of physics). Currently, this micro-macro connection is known only for systems in thermal equilibrium systems, and forms the foundation for textbook thermodynamics, statistical physics, and much of modern technology. Due to the complexity of this challenge, a typical approach in physics is to study simple model systems, with the hope that enough insight can be gained for us to make a good attempt at the next step: formulating a theory. Our research focus on working with well-known models (e.g., Ising, totally asymmetric exclusion process, etc.), as well as building novel simple systems. All are motivated by not only pure mathematics but also natural systems all around us. Our short term goal is to find new principles for non-equilibrium statistical physics. As an example, an important one may be labeled as ‘negative response’: Ordinarily, we expect a system to ‘go further’ when ‘pushed harder.’ Yet, under many far-from-equilibrium conditions, we can expect otherwise. Indeed, one of the articles we published is entitled Getting more from pushing less (published in the American Journal of Physics in 2002). In this present project, we discovered similarly surprising behavior in several simple models of biological transport processes, social networks, epidemic spreading, and global heat transfer. A slightly more technical description of our research focus is the presence of persistent probability currents in non-equilibrium steady states. Completely absent in systems in thermal equilibrium, these currents are associated with significant implications, as they give rise to measurable observables, such as energy/matter flux through a system, entropy production, and rotations in the space of macroscopic quantities. A concrete example of our recent explorations is the emergence of mass convection loops in the absence of gravity or shear, when a simple model of particles moving on a lattice (Ising lattice gas) is coupled to two thermal reservoirs. We firmly believe that such explorations will lead us to novel, key concepts crucial to the foundations of a viable theory of non-equilibrium statistical mechanics. Since non-equilibrium processes are central to science and technology, fundamental theoretical progress will reverberate far beyond the borders of condensed matter theory, with implications for, e.g., the life sciences, chemistry, and environmental science/engineering. Of equal importance, this project offers wide-ranging research, education, and collaborative opportunities to junior researchers at all levels, from high school interns to experienced postdoctoral associates. They not only learn about significant frontiers of modern physics but also acquire important skills which are valued in other disciplines, such as high-performance parallel computing, writing efficient codes, scrutinizing problems with analytic eyes and minds, as well as building effective models for previously unknown natural processes. As a result, many members of our group have been successful, e.g., undergraduates winning prestigious national scholarships and fellowships, while PhD students and postdoctoral associates moving on to hold key positions in academia and the corporate world.
