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Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique created in order to construct nonlinear evolution equations describing non-equilibrium processes, while also developing a geometric context for non-equilibrium thermodynamics. Solid materials are the main focus in this volume, but the construction is shown to also apply to fluids. This volume also:-Explains the theory behind thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes-Provides a geometric setting for non-equilibrium thermodynamics through several standard models, which are defined as maximum dissipation processes-Emphasizes applications to the time-dependent modeling of soft biological tissueMaximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure will be valuable for researchers, engineers and graduate students in non-equilibrium thermodynamics and the mathematical modeling of material behavior.
List of contents
History of Non-Equilibrium Thermodynamics.- Energy Methods.- Evolution Construction for Homogeneous Thermodynamic Systems.- Viscoelasticity.- Viscoplasticity.- The Thermodynamic Relaxation Modulus as a Multi-scale Bridge from the Atomic Level to the Bulk Material.- Contact Geometric Structure for Non-equilibrium Thermodynamics. Bifurcations in the Generalized Energy Function.- Evolution Construction for Non-homogeneous Thermodynamic Systems.- Electromagnetism and Joule Heating.- Fracture.
Summary
Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique created in order to construct nonlinear evolution equations describing non-equilibrium processes, while also developing a geometric context for non-equilibrium thermodynamics. Solid materials are the main focus in this volume, but the construction is shown to also apply to fluids. This volume also:
• Explains the theory behind thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes
• Provides a geometric setting for non-equilibrium thermodynamics through several standard models, which are defined as maximum dissipation processes
• Emphasizes applications to the time-dependent modeling of soft biological tissue
Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure will be valuable for researchers, engineers and graduate students in non-equilibrium thermodynamics and the mathematical modeling of material behavior.
Report
From the reviews:
"The author presents his construction of a geometric model for non-equilibrium thermodynamics and his maximum dissipation criterion which is assumed to complement the second law of thermodynamics. ... the author explores different concrete situations where his construction of a maximum dissipation criterion may be applied. ... This book will be interesting for researchers involved either in applied mathematics or in mechanics." (Alain Brillard, Zentralblatt MATH, Vol. 1222, 2011)
