Integrated Calendar

A Brownian motor rectifies thermal noise and creates useful work. Here we address how this machine can emerge without predefined energy minimum in a system out of thermal equilibrium. Intuitively, Brownian motor as any artificial or biological machine should degrade with time. I will show that on contrary, a system with multiple degrees of freedom out of thermal equilibrium can be stable at a state that generates useful work.

It is demonstrated with the help of ab initio analysis of a modified Feynman-Smoluchowski ratchet with two degrees of freedom. Out of thermal equilibrium, an environment imposes effective mechanical forces on nano-fabricated devices as well as on microscopic chemical or biological systems. Thus out of thermal equilibrium environment can enforce a specific steady state on the system by creating effective potentials in otherwise homogeneous configuration space.

I present an ab initio path from the elastic scattering of a single gas particle by a mechanical system to the transition rate probability between the states of the system with multiple degrees of freedom, together with the corresponding Masters-Boltzmann equation and the average velocities of the system’s degrees of freedom as functions of the macroscopic parameters of the out-of-equilibrium environment. It results in Onsager relations that include the influence of the different degrees of freedom on each other.

An interesting finding is that some of these forces persist even in a single temperature environment if the thermodynamic limit does not hold. In addition, the spatial asymmetry of the system’s stable state, together with the corresponding directed motion, may possess preferred chiral symmetry.

Simple 2-dimensional cut and fold patterns can be transformed into 3-dimensional shapes upon stretch-ing. We use this simple approach to develop mechanical metamaterials with several interesting proper-ties and applications. I will describe ways of tuning properties via geometric structure, and discuss ex-amples of how this can be used to achieve superior performance in mechanics, photonics, electronics, sensors, and other areas.

References:
“Dynamic kirigami structures for integrated solar tracking.” Nature Comm. 6, 8092 (2015)
“A kirigami approach to engineering elasticity in nanocomposites through patterned defects.” Na-ture Mater., 14 (2015) 785
“An Electric Eel-Inspired Artificial Soft Power Source from Stacked Hydrogels.” Nature, 552 (2017) 214

Methods of statistical physics allow to explore the quantitative nexus among economic growth of a country, diversity of its productions, and evolution in time of its export basket(*). A stochastic model of evolution, calibrated on data for 1238 exports from 223 countries in 21 years, enables counterfactual analyses based on estimates of the part of growth due to resource transfers between different productions. Original use of the Boltzmann-Shannon entropy function leads to the construction of consistent measures of the efficiency of national
economies and of the specialization of productions. Comparisons with dynamical and GDP pc data lead to clear distinctions among developed, developing, underdeveloped and risky countries. Perspective applications of the entropic measures in other fields (ecology, microbiology,..) where diversity has to be estimated from bipartite networks will be shortly outlined.

(Work in collaboration with G. Teza, University of Padova, and M. Caraglio, Katholieke Universiteit Leuven.)