Systems far from equilibrium: relaxation processes and steady-state properties

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education toward developing a theory of systems far from the unchanging and familiar state of equilibrium. Nonequilibrium phenomena are omnipresent and range from weather patterns to life itself. For systems that are out of equilibrium two complementary aspects, both equally relevant, can be distinguished. These are stationary states, wherein the system will remain if not pushed from the outside, and the relaxation towards these stationary states. Gaining a better understanding of both the stationary properties and the relaxation processes are needed in order to fully understand the world around us, and to develop new ways to use these processes for tailoring the properties of various systems of interest, ranging from novel materials to biological systems and ecosystems. The study of systems far from equilibrium poses many challenges, both on the fundamental and on the practical level. Whereas there is a well-established theoretical framework for equilibrium systems, a similar comprehensive framework for non-equilibrium systems and processes remains elusive. This project aims at exploiting a variety of analytical and numerical techniques to advance understanding of non-equilibrium phenomena. The project covers both fundamental and applied aspects. One important activity focuses on the investigation of the stability of food webs to various perturbations, as for example species extinction, species migration or seasonal changes. Related to this is the question of ecomanagement and the targeted intervention in predator-prey systems in order to achieve specific goals, as for example maintaining biodiversity or removing a detrimental species. Another activity investigates the relaxation properties in model systems used to describe synchronization phenomena in biology. This investigation will allow to explore possible relationships between physical and biological aging. The project is designed so that both undergraduate and graduate students can learn and contribute in a substantial and meaningful way. This training through research approach allows to involve students at every level in cutting-edge research projects. TECHNICAL SUMMARY This award supports theoretical research and education toward developing a theory of systems far from equilibrium. Non-equilibrium processes in nature and in human activities, such as making and processing materials, abound, and a unifying theoretical description of non-equilibrium interacting many-body systems remains elusive. The study of specific model systems can lead to progress in understanding systems far from equilibrium through revealing universal properties, using the large toolbox of numerical and analytical methods provided by statistical physics. The PI will combine advanced analytical and numerical techniques to address fundamental questions and potential applications of systems far from equilibrium through three different research thrusts. The first research thrust focuses on directed spin models that are prototypical examples of system that evolve to the equilibrium Boltzmann-Gibbs distribution even though detailed balance is violated due to the irreversibility of the dynamics. Preliminary results for the two-dimensional directed Ising model show that in the low temperature phase directedness yields a remarkable acceleration of the dynamics, manifested by a change in the value of the dynamical exponent. The research on directed spin models, addresses both fundamental aspects, such as change in dynamic properties due to irreversibility, and applied aspects, such as algorithmic tools to accelerate convergence to equilibrium. New insights into the properties of systems that violate detailed balance but fulfill the weaker condition of global balance are expected to result. For some classes of systems, directed models have the potential to become an algorithmic tool to accelerate convergence to equilibrium, which could have impact on many disciplines. The second research thrust proposes to investigate relaxation processes and the responses to perturbations in many-species systems. Food webs, discussed in the context of population dynamics, allow to gain insights into generic issues related to biodiversity and species extinction. Many of these food webs exhibit remarkable space-time patterns in a spatial setting that warrant an in-depth characterization. The PI plans (1) to study the stability of an ecological system, more specifically its response to perturbations, both small and large, and how it relaxes to the steady state, and (2) to investigate the control of an ecology, for example in order to assure biodiversity and avoid species extinction. Optimal control theory will be exploited as an analytical tool for understanding targeted interventions in predator-prey systems. This study is expected to yield valuable insights into the ecomanagement of non-trivial food webs. The third research thrust is devoted to the study of physical aging in coupled classical rotators. Coupled classical rotators and related systems present a class of systems with dynamic properties reminiscent of spin glasses. The PI will study the aging properties of these systems, investigate their responses to perturbations, and explore the existence of memory and rejuvenation effects. This study of coupled oscillators and related systems, with known biological applications, will provide an opportunity to explore possible relationships between physical and biological aging. Due to the ubiquity of non-equilibrium processes in nature, this research project may have impact beyond the boundaries of condensed matter physics. Gaining a better understanding of transient and steady-state properties in systems amenable to an in-depth investigation using the large toolbox of statistical physics should contribute to the development of a more general theory that describes systems far from equilibrium. This project is designed so that both undergraduate and graduate students can learn and contribute in a substantial and meaningful way. This training through research approach allows to involve students at every level in cutting-edge research projects.