Present day science and technology ever more frequently deal with nanometric objects, with many fewer elementary constituents than Avogadro's number but large enough to nonetheless require a statistical approach. In particular, in such small systems, fluctuations cannot be neglected, and standard thermodynamic notions are not directly applicable. Therefore, a statistical theory is needed for systems such as molecular motors, granular fluids and transport in highly confining or low-dimensional media. For instance, the known features of Gaussian processes, effective diffusive equations and the usual reaction-diffusion equations fail when the ratio of mean free path to typical system size is large, and transport of particles is dominated by collisions with walls. Translocation processes across nanopores, and more general transport of biological and nano-technological interest, are of this kind. Nevertheless, the relation between diffusion and response is not trivial in such anomalous cases. Analogously, modern transistors measure just a few nanometers, a scale at which heat management (a bottleneck in improving ICT devices) cannot be based on the notions of energy efficiency, and the general laws of heat and work transformations need rethinking. Similar difficulties are encountered in nanopore molecular biosensing; e.g., for fast and cheap DNA sequencing. Although DNA sequencing is relatively well developed, for proteins the goal is far from achieved, despite its unquestionable interest in fundamental science, technology and medicine.

The first part of our program (Jul 25--Aug 19, 2016) will emphasize transport phenomena (from ergodic theory to nanotechnology), while the second part (Aug 8--Sep 2, 2016) will focus on information processing in nonequilibrium statistical mechanics, engineering and biology. In the central weeks of August, a joint workshop will be devoted to the many aspects of common interest.

**Part 1. FPU, billiards and anomalous transport: from ergodic theory to Nanotechnology**

Many aspects of nanoscale transport phenomena require deeper understanding, such as the response of a system to external driving and its connection with the statistical fluctuations of microscopic quantities. What happens to energy or charge transport in systems that are effectively 1-dimensional, such as nanowires? How could one act on the microscopic degrees of freedom of a given system, as present technology is becoming able to do, in order to obtain desired transport properties? To answer questions such as these, the variety and complexity of specific interactions that one should consider begin with the investigation of simplified models. Such models have proved invaluable for the study of transport and play a major role in the present studies of systems in reduced dimensions. Among widely studied models, a prominent role is played by the chains of oscillators originally considered by Fermi, Pasta and Ulam, and by “billiards” -- systems of non-interacting particles moving in chaotic or non-chaotic fashions. These theoretical models have served the scientific community in various ways, providing mathematical benchmarks for ergodic and dynamical systems theory, showing how normal and anomalous transport phenomena can be established and related to each other, suggesting technological advances, e.g. in the development of nano-devices and thermal rectifiers. The first four weeks of the workshop will bring together experts from the mathematical, theoretical and experimental communities, in order to promote further advances in all these fields.

**Key subjects: **

* The physics behind normal and anomalous transport, and its technological, bio-physical and bio-medical implications, with possible experimental measurement advancement;

* The general theory of response to perturbations and transport phenomena in the framework of non-equilibrium physics, and connections with fluctuation relations;

* Novel approaches to the mathematics of ergodic theory and its physical relevance.

**Part 2. Information Processing at the Nanoscale **

Recent work has established close connections between information theory and small systems operating in fluctuating environments. These systems include artificial devices such as the transistors or quantum dots typically considered in physics and engineering, as well as the molecular motors or networks of chemical reactions at work in living systems. Despite the significant differences among these systems, they share common features connected with information processing, and they deal with common issues of energetic cost, accuracy, and robustness. The goal of this part of the program is to bring together key experts from the different communities working on these questions, to make progress towards a unified understanding of information processing at small scales. In particular, we aim to connect researchers in statistical physics, feedback and control engineering, and biophysics.

**Key subjects:**

* Assessing the role of information in thermodynamics; clarifying recently developed perspectives of information as a thermodynamic resource;

* Uniting common approaches to the control of small-scale systems from physics, control engineering, and communications engineering, in particular uniting the somewhat disparate approaches taken to describe fundamental limitations on control performance;

* Analyzing information processing at small scales in biology with an emphasis on fundamental tradeoffs among energy, speed, and accuracy; identifying potential commonalities between problems such as chemotaxis, sensing, kinetic proofreading, signal transduction.

Except the central weeks of the program, the number of talks will not exceed two per day, leaving a plenty of time for interactions and collaborations.