## Beyond the Second Law: Entropy Production and Non-equilibrium SystemsRoderick C. Dewar, Charles H. Lineweaver, Robert K. Niven, Klaus Regenauer-Lieb The Second Law, a cornerstone of thermodynamics, governs the average direction of dissipative, non-equilibrium processes. But it says nothing about their actual rates or the probability of fluctuations about the average. This interdisciplinary book, written and peer-reviewed by international experts, presents recent advances in the search for new non-equilibrium principles beyond the Second Law, and their applications to a wide range of systems across physics, chemistry and biology. Beyond The Second Law brings together traditionally isolated areas of non-equilibrium research and highlights potentially fruitful connections between them, with entropy production playing the unifying role. Key theoretical concepts include the Maximum Entropy Production principle, the Fluctuation Theorem, and the Maximum Entropy method of statistical inference. Applications of these principles are illustrated in such diverse fields as climatology, cosmology, crystal growth morphology, Earth system science, environmental physics, evolutionary biology and technology, fluid turbulence, microbial biogeochemistry, plasma physics, and radiative transport, using a wide variety of analytical and experimental techniques. Beyond The Second Law will appeal to students and researchers wishing to gain an understanding of entropy production and its central place in the science of non-equilibrium systems – both in detail and in terms of the bigger picture. |

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### Contents

3 | |

Part IITheoretical Perspectives on Entropy Production | 28 |

Its Relationship to Entropy Production Theorems for Nonequilibrium Systems and Observations on Its Extrema | 29 |

3 A Theoretical Basis for Maximum Entropy Production | 49 |

4 Dissipation Rate Functions Pseudopotentials Potentials and Yield Surfaces | 72 |

272293_1_En_5_Chapter_OnlinePDF | 97 |

6 The Time Evolution of Entropy Production in Nonlinear Dynamic Systems | 113 |

7 Control Volume Analysis Entropy Balance and the Entropy Production in Flow Systems | 129 |

12 Entropy ProductionBased Closure of the Moment Equations for Radiative Transfer | 241 |

13 MaxEP and Stable Configurations in FluidSolid Interactions | 257 |

14 Can the Principle of Maximum Entropy Production be Used to Predict the Steady States of a RayleighBérnard Convective System? | 277 |

15 Bifurcation Stability and Entropy Production in a SelfOrganizing FluidPlasma System | 291 |

16 MaxEnt and MaxEP in Modeling Fractal Topography and Atmospheric Turbulence | 308 |

17 Entropic Bounds for MultiScale and MultiPhysics Coupling in Earth Sciences | 323 |

18 Use of Receding Horizon Optimal Control to Solve MaxEPBased Biogeochemistry Problems | 337 |

19 Maximum Entropy Production and Maximum Shannon Entropy as Germane Principles for the Evolution of Enzyme Kinetics | 360 |

Maximum Power Limits Dissipative Structures and Planetary Interactions | 163 |

Part IIIApplications to Nonequilibrium Systems | 183 |

9 Predictive Use of the Maximum Entropy Production Principle for Past and Present Climates | 184 |

10 Thermodynamic Insights into Transitions Between Climate States Under Changes in Solar and Greenhouse Forcing | 201 |

11 Entropy Production in Planetary Atmospheres and Its Applications | 224 |

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