The characteristic features of solid oxide fuel cells are reviewed from the viewpoint of the thermodynamic variables to be developed inside cells/stacks particularly in terms of gradients of chemical potential, electrical potential and temperature and corresponding flows of air, fuel, electricity and heat. Examples of abrupt destruction of SOFC systems were collected from failures in controlling their steady flows, while continuous degradation was caused by materials behaviors under gradients of chemical potentials during a long operation. The local equilibrium approximation has been adopted in NEDO project on the durability/reliability of SOFC stacks/systems; this makes it possible to examine the thermodynamic stability/reactivity as well as mass transfer under the thermodynamic variable gradients. Major results of the NEDO project are described with a focus on degradation/deterioration of electrolyte and electrode materials.