  A new mesoscopic non-equilibrium thermodynamic approach is developed. The
approach is based on the thermodynamic identity associated the first and second
law of thermodynamics. In the framework of the approach different internal
dissipative channels of energy are taken in account in an explicit form,
namely, the thermal channel and channels of defect subsystems. The identity has
a perfect differential form what permits to introduce an extended
non-equilibrium state and use the good developed mathematical formalism of
equilibrium and non-equilibrium thermodynamics. The evolution of
non-equilibrium variables of a physical system are described by a Landau-based
equation set expressed through internal or different kinds of free energy
connected by means of the Legendre transforms. The accordance between the
different kinds of energy is possible owing to introduction of some trends into
the equation subset described the defect subsystems and having a nature of
structural viscosity. The possibilities of the approach are illustrated on the
example of quasibrittle solid damage and failure. Taking into account only one
type of defects (viz., microcracks) and mechanical parameters in an expansion
of free energy down to third powers in relative to average energy per
microcrack, the description of destruction of quasi-brittle solids during
long-term loading is considered. The consideration allows to find equilibrium
and non-equilibrium values of the free energy. A qualitative behavior of the
system on parameters of the theory is analyzed. The destruction of material is
described from the uniform positions, both at uniform tension and uniaxial
compression. Origins of the high stability of mine workings at small depths and
their instability at large depths are explained.
