Contents -- Preface -- 1 The phenomenology of complex systems -- 1.1 Complexity, a new paradigm -- 1.2 Signatures of complexity -- 1.3 Onset of complexity -- 1.4 Four case studies -- 1.4.1 Rayleigh-B enard convection -- 1.4.2 Atmospheric and climatic variability -- 1.4.3 Collective problem solving: food recruitment in ants -- 1.4.4 Human systems -- 1.5 Summing up -- 2 Deterministic view -- 2.1 Dynamical systems, phase space, stability -- 2.1.1 Conservative systems -- 2.1.2 Dissipative systems -- 2.2 Levels of description -- 2.2.1 The microscopic level -- 2.2.2 The macroscopic level -- 2.2.3 Thermodynamic formulation -- 2.3 Bifurcations, normal forms, emergence -- 2.4 Universality, structural stability -- 2.5 Deterministic chaos -- 2.6 Aspects of coupling-induced complexity -- 2.7 Modeling complexity beyond physical science -- 3 The probabilistic dimension of complex systems -- 3.1 Need for a probabilistic approach -- 3.2 Probability distributions and their evolution laws -- 3.3 The retrieval of universality -- 3.4 The transition to complexity in probability space -- 3.5 The limits of validity of the macroscopic description -- 3.5.1 Closing the moment equations in the mesoscopic description -- 3.5.2 Transitions between states -- 3.5.3 Average values versus uctuations in deterministic chaos -- 3.6 Simulating complex systems -- 3.6.1 Monte Carlo simulation -- 3.6.2 Microscopic simulations -- 3.6.3 Cellular automata -- 3.6.4 Agents, players and games -- 3.7 Disorder-generated complexity -- 4 Information, entropy and selection -- 4.1 Complexity and information -- 4.2 The information entropy of a history -- 4.3 Scaling rules and selection -- 4.4 Time-dependent properties of information. Information entropy and thermodynamic entropy -- 4.5 Dynamical and statistical properties of time histories. Large deviations, uctuation theorems.

4.6 Further information measures. Dimensions and Lyapunov exponents revisited -- 4.7 Physical complexity, algorithmic complexity, and computation -- 4.8 Summing up: towards a thermodynamics of complex systems -- 5 Communicating with a complex system: monitoring, analysis and prediction -- 5.1 Nature of the problem -- 5.2 Classical approaches and their limitations -- 5.2.1 Exploratory data analysis -- 5.2.2 Time series analysis and statistical forecasting -- 5.2.3 Sampling in time and in space -- 5.3 Nonlinear data analysis -- 5.3.1 Dynamical reconstruction -- 5.3.2 Symbolic dynamics from time series -- 5.3.3 Nonlinear prediction -- 5.4 The monitoring of complex fields -- 5.4.1 Optimizing an observational network -- 5.4.2 Data assimilation -- 5.5 The predictability horizon and the limits of modeling -- 5.5.1 The dynamics of growth of initial errors -- 5.5.2 The dynamics of model errors -- 5.5.3 Can prediction errors be controlled? -- 5.6 Recurrence as a predictor -- 5.6.1 Formulation . -- 5.6.2 Recurrence time statistics and dynamical complexity -- 5.7 Extreme events -- 5.7.1 Formulation -- 5.7.2 Statistical theory of extremes -- 5.7.3 Signatures of a deterministic dynamics in extreme events -- 5.7.4 Statistical and dynamical aspects of the Hurst phenomenon -- 6 Selected topics -- 6.1 The arrow of time -- 6.1.1 The Maxwell-Boltzmann revolution, kinetic theory, Boltzmann's equation -- 6.1.2 First resolution of the paradoxes: Markov processes, master equation -- 6.1.3 Generalized kinetic theories -- 6.1.4 Microscopic chaos and nonequilibrium statistical mechanics -- 6.2 Thriving on uctuations: the challenge of being small -- 6.2.1 Fluctuation dynamics in nonequilibrium steady states revisited -- 6.2.2 The peculiar energetics of irreversible paths joining equilibrium states -- 6.2.3 Transport in a uctuating environment far from equilibrium.

6.3 Atmospheric dynamics -- 6.3.1 Low order models -- 6.3.2 More detailed models -- 6.3.3 Data analysis -- 6.3.4 Modeling and predicting with probabilities -- 6.4 Climate dynamics -- 6.4.1 Low order climate models -- 6.4.2 Predictability of meteorological versus climatic fields -- 6.4.3 Climatic change -- 6.5 Networks -- 6.5.1 Geometric and statistical properties of networks -- 6.5.2 Dynamical origin of networks -- 6.5.3 Dynamics on networks -- 6.6 Perspectives on biological complexity -- 6.6.1 Nonlinear dynamics and self-organization at the biochemical, cellular and organismic level -- 6.6.2 Biological superstructures -- 6.6.3 Biological networks -- 6.6.4 Complexity and the genome organization -- 6.6.5 Molecular evolution -- 6.7 Equilibrium versus nonequilibrium in complexity and self-organization -- 6.7.1 Nucleation -- 6.7.2 Stabilization of nanoscale patterns -- 6.7.3 Supramolecular chemistry -- 6.8 Epistemological insights from complex systems -- 6.8.1 Complexity, causality and chance -- 6.8.2 Complexity and historicity -- 6.8.3 Complexity and reductionism -- 6.8.4 Facts, analogies and metaphors -- Color plates -- Suggestions for further reading -- Index.