In an open system, there is an exchange of energy and matter between the system and the surroundings. The presence of reactants in an open beaker is an example of an open system. Here the boundary is an imaginary surface enclosing the beaker and reactants. It is named closed, if borders are impenetrable for substance, but allow transit of energy in the form of heat, and isolated, if there is no exchange of heat and substances. The open system cannot exist in the equilibrium state. To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables that was described above, a set of internal variables   have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of non-equilibrium of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable
where   is a relaxation time of a corresponding variable. It is convenient to consider the initial value   equal to zero.
The specific contribution to the thermodynamics of open non-equilibrium systems was made by Ilya Prigogine, who investigated a system of  chemically reacting substances. In this case  the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalized, to consider any deviations from the equilibrium state,  such as   structure of the system, gradients of temperature, difference of concentrations of substances and so on, to say nothing of degrees of completeness of all chemical reactions,   to be  internal variables. 
The increments  of Gibbs free energy     and entropy   at  and  are determined as 
The stationary states of the  system exist due to exchange of both thermal energy   and a stream of particles. The sum of the last terms in the equations presents the total energy coming into the system with the stream of particles of substances    that can be positive or negative; the quantity   is chemical potential of substance .     The middle terms in equations (2) and (3) depict energy dissipation (entropy production) due to the relaxation of internal variables ,  while  are  thermodynamic forces.
This approach to the open system allows describing the growth and development of living objects in thermodynamic terms.