Maximum Dissipation Non-Equilibrium Thermodynamics and Its Geometric Structure

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.

Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique 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 a thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes, based on supplementing the second law with a maximum dissipation criterion

• Provides a geometric setting for non-equilibrium thermodynamics in differential topology and, in particular, contact structures that generalize Gibbs

• Models processes that include thermoviscoelasticity, thermoviscoplasticity, thermoelectricity and dynamic fracture

• Recovers several standard time-dependent constitutive models as maximum dissipation processes

• Produces transport models that predict finite velocity of propagation

• 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.