Vladimir Pokrovskii

Pokrovskii was born May 11, 1934, into a Russian family in the rural locality Altayskoye, Altaysky District, Altai Krai (Russian: Алтайское, Алтайского края), Russia.^{[citation needed]} He graduated from Tomsk State University in Siberia as a physicist (Department of Theoretical Physics) in 1958 and in the same year was employed as a teacher of physics at Tomsk Polytechnic University.^{[citation needed]} In 1964 he moved to the Branch of Institute of Chemical Physics of the Academy of Sciences of the USSR (Chernogolovka, Moscow region) where in positions of Senior Research Fellow was engaged in studying of suspensions and polymers. He received the first Russian scientific degree (Candidate of Sciences, 1968) and the second Russian Degree (Doctor of Sciences, 1977) in Physics and Mathematics.^{[citation needed]} Since 1980 Vladimir Nikolaevich has managed the Department of Applied Mathematics of the Altai Polytechnic Institute (now Altai State Technical University), (Barnaul, Russia), and in 1981 he was appointed Professor of Applied Mathematics.^{[citation needed]} From 1987-1995 he was Professor and Head of the Department of Applied Mathematics at Moscow University of Economics, Statistics and Informatics (МЭСИ, the Russian abbreviation). He works on methods of modelling of economic processes and undertakes the studies in the field of the mathematical description of economic growth which has led to the understanding of the role of energy and, eventually, to the formulation of the generalized labour theory of value.^{[citation needed]}

Since 1995 Vladimir Nikolaevich has been a visiting professor at Maltese University. He gives lectures on statistical physics and is engaged in research work. He now (2021) lives with his wife in Moscow, and writes about his life in 'Notes'^[1]

Jubilee Medal "In Commemoration of the 100th Anniversary of the Birth of Vladimir Ilyich Lenin" (1970) ^{[citation needed]}

Dynamics of suspensions

For description of dynamic behaviour of polymer solutions and molecular liquids, suspensions of rigid or semi-rigid particles were used as simple heuristic models that allowed to connect the properties of moving systems with structural characteristics. The constitutive equations of the flowing dilute suspension of rigid ellipsoids was apparently the first example of microrheological constitutive equations of complex fluid.^[2][3] The usage of rigid ellipsoids model was also helpful in explaining of optical anisotropy and relaxation phenomena of the molecular systems.^[4] The suspension of rigid particles in an anisotropic fluid provides a qualitative description of behaviour of liquid crystals^[5][6]

Polymer dynamics

The properties of polymers, according to earlier hypothesis by Sam Edwards and Pierre-Gilles de Gennes, could be explained by a special movement of long macromolecule among other macromolecules like a snake (via reptation). The development of the theory of stochastic thermal motion of long macromolecules among similar macromolecules (in the entangled system) confirms the existence of reptation in the region of molecular mass above 10 times the length between 'entanglements'^[7][8] and identifies the internal relaxation processes in polymers from the molecular point of view.^[9] The theory has determined the reliable foundation for the theory of viscoelasticity, diffusion and a number of other features of polymeric materials.^[10] The Pokrovskii's monograph is included into the Sunfoundry list of the best books on dynamics of polymers.^[11] The theory is concerned with linear macromolecules, and one needs in the extension of the theory to macromolecules of different structures (in a form of a comb, a star, and others).

Econodynamics

The Technological theory of social production is based on the achievements of classical political economy and presents a clarification of the conventional, neoclassical theory of economic growth. The theory is formulated as empirical science on the creation, motion and disappearance of value.^[12][13] Considering production factors, econodynamics regards two distinctive characteristics of the production equipment: capital stock as value of production equipment (production capital) and capital service as a substitute for labour. Capital service is considered, in line with workers' efforts, as an independent production factor, whereas capital stock is considered to be the means of attracting labour and energy services to the production. Human effort and the work of external energy sources appears to be the true sources of value; productivity of capital is eventually productivity of working people and substitutive work. It has led to the understanding of the role of energy and, eventually, to the generalization of the labour theory of value. The theory allows analysis of the current situation in economies and to reconstruct the picture of production activity on the Earth in the previous millennia.

Dynamics of complex thermodynamic systems

Considering the complex systems, such as polymers, living organisms, social organisations and so on, to be thermodynamic systems with some internal structure, the principles of nonequilibrium thermodynamics have been reformulated, using the concept of internal variables that describe deviations of a thermodynamic system from the equilibrium state.^[14][15][16] Considering the first law of thermodynamics, work of internal variables is introduced and internal thermal energy of non-equilibrium systems is taken into account. It is shown that the requirement that the thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. These statements, in line with the axioms introducing internal variables can be considered as basic principles of nonequilibrium thermodynamics. It is shown that known linear parities between thermodynamic forces and fluxes and also the entropy production, as a sum of products of thermodynamic forces and fluxes, are consequences (valid only in linear area and for steady-state situations) of fundamental principles of thermodynamics. Among the numerous applications of non-equilibrium thermodynamics, it appears to be a description of living organism as an open thermodynamic system, which allows formulating the thermodynamic equation of growth^[17]