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Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

Continuum mechanics. --- Scaling laws (Statistical physics). --- Calculus --- Atomic Physics --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Scaling laws (Statistical physics) --- Statistical mechanics. --- Micromechanics. --- Mechanics of continua --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Mathematics. --- Dynamics. --- Ergodic theory. --- Physics. --- Dynamical Systems and Ergodic Theory. --- Mathematical Methods in Physics. --- Composite materials --- Solid state physics --- Microstructure --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Mechanics --- Quantum statistics --- Statistical physics --- Thermodynamics --- Physical laws --- Ranking and selection (Statistics) --- Differentiable dynamical systems. --- Mathematical physics. --- Physical mathematics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Force and energy --- Statics