Many modern technologies rely on complex phenomena in systems out of equilibrium. Some of the most interesting phenomena arise in small systems in which fluctuations play a prominent role and the usual laws of (equilibrium) statistical mechanics do not work. This project focuses on thermodynamic efficiency in small non-equilibrium devices, and on mesoscopic descriptions of reaction-subdiffusion problems,in which nonlinearity, stochasticity, and complexity away from equilibrium are important. The Fluctuation theorem specifies the probability of fluctuations that cause a system to become more ordered, an effect that is observable if a system is sufficiently small. This project will examine whether the Fluctuation theorem can reveal something about the efficiency of small systems in the non-equilibrium regime, and whether the ideas of finite time and stochastic thermodynamics can be used to establish new universal results. These questions will be addressed for mechanical and chemical transport in the classical regime and, most importantly, for transport properties in the quantum regime. The focus in the classical regime will include transport via effusion, and the microscopic description of a chemically driven Brownian motors and pumps. In the quantum regime the foci include transport of particles through quantum dots and the relation of the fluctuation theorem to the theory of quantum measurement. Universality of nonlinear responses that encompass both regimes will be sought. Measures to differentiate among various subdiffusive scenarios such as motion in a fractal medium versus motion in a regular medium with quenched disorder will be sought. A number of analytic and numerical methods will be applied. While some of the numerical methods are standard, others will involve the development of multiscale approaches that can handle the range of spatial and temporal scales required for this work. Solution of the problems posed in this proposal will lead to new insights to questions that have seen an explosive growth of interest with the development of new theoretical, experimental, and numerical methods.
The broader impact of this work has two aspects. One is the close and extensive involvement of members of underrepresented groups. The participants in this efort have long track records in mentoring undergraduate, graduate, and postgraduate research of members of underrepresented groups and designing a variety of institutional initiatives to enhance that. They have a strong commitment to continue these efforts. Another direction lies in the extensive collaborative interdisciplinary network that the investigators have successfully established with scientists in Europe and Latin America. This is made possible by the essential role of one of the senior investigators as one of three conveners of a major European Science Foundation effort in statics and dynamics, and the involvement of the P.I. with scientists in Latin America.
