Optimality of nonequilibrium systems and problems of statistical thermodynamics

This paper reviews advantages which stem from using methods of optimal control theory and variational calculus in nonequilibrium thermodynamics of transport phenomena, focusing on selected problems of statistical thermodynamics rather than on typical phenomenological descriptions. Neglected are aspects of thermodynamic stability and oscillatory phenomena, as those frequently considered earlier. The main problems discussed here are: statistical aspects of nonequilibrium conservation laws, work-producing devices described by master equations, and development of living systems governed by a complexity criterion based on information-theoretic entropy. These problems are presented mainly from the viewpoint of the contribution of the author and some associated researchers, yet an attempt is made to give a comparison of our results with those following from main work of others.