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.

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.