The authors provide a theoretical description of the system and propose a method for calculating the optimal directions of innovation management, which allows us to give a comprehensive assessment of the adopted innovative solutions and indicate the reasons hindering effective innovation activity. This research examines energy-entropic methods for evaluating the efficiency of production and management, as an effective method of managing innovation, mainly by optimizing the use of energy consumed based on the achievements of science and technology. The proposed entropic assessment of the state of the parameters of the production system provides the possibility of assessing the change in the state of these parameters by a single relative indicator and the synthesis of these estimates into a single economic image of the current production situation.

1. http://www.iaeme.com/IJMET/index.asp 1413 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 1413-1419, Article ID: IJMET_10_01_143
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=01
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
ENERGY-ENTROPY MODEL FOR ASSESSMENT
OF ECONOMIC SYSTEM MANAGEMENT
Natalia Natocheeva
D.Sc. (Economics), Professor, Plekhanov Russian University of Economics,
Moscow, Russian Federation.
Ludmila Goloshchapova
Ph. D., associate Professor Plekhanov Russian University of Economics, Moscow, Russian
Federation
Olga Veremeeva
Ph. D., Tax and Budget Legislation of the Institute of Legislation and Comparative Law under
the Government of the Russian Federation, Russian Federation, Moscow.
Marianna Nazaeva
Ph. D., associate Professor, Chechen State Pedagogical University, Russian Federation,
Grozniy.
Victor Moroz
Phd, Financial University under the Government of the Russian Federation, Moscow, Russian
Federation.
ABSTRACT
The authors provide a theoretical description of the system and propose a method for
calculating the optimal directions of innovation management, which allows us to give a
comprehensive assessment of the adopted innovative solutions and indicate the reasons
hindering effective innovation activity. This research examines energy-entropic methods
for evaluating the efficiency of production and management, as an effective method of
managing innovation, mainly by optimizing the use of energy consumed based on the
achievements of science and technology. The proposed entropic assessment of the state
of the parameters of the production system provides the possibility of assessing the change
in the state of these parameters by a single relative indicator and the synthesis of these
estimates into a single economic image of the current production situation.
Key words: energy-enthropy processes, industrial production, innovation process, law of
energy-entropy, entropy calculation, and economic efficiency.

2. Natalia Natocheeva, Ludmila Goloshchapova, Olga Veremeeva, Marianna Nazaeva and Victor Moroz
http://www.iaeme.com/IJMET/index.asp 1414 editor@iaeme.com
Cite this Article: Natalia Natocheeva, Ludmila Goloshchapova, Olga Veremeeva,
Marianna Nazaeva and Victor Moroz, Energy-Entropy Model for Assessment of Economic
System Management, International Journal of Mechanical Engineering and Technology,
10(01), 2019, pp.1413–1419
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&Type=01
1. INTRODUCTION
The rapid increase in the volume of incoming and processed information in oil companies has led
to a change in not only the automation of the process of data processing and research, but also in
the intellectualization of informational and organizational processes, building and implementing
effective methods and intellectual supporting technologies of decision-making [1]. Ensuring the
economic growth of the country urgently requires the widespread use of innovation processes as
the most important factor of national development, primarily in industrial production. This is
possible with the development and introduction of new approaches to the consideration of
innovative efficiency of industrial production with the active use of key achievements of
scientific and technological progress and the formation of a new mechanism for managing
innovation activities at all levels of the national economy and individual enterprises.
The formation of a market economy makes it necessary to study a variety of issues, among
which it is necessary to specifically emphasize the assessment of production efficiency. The
urgency of the problem posed is explained by the fact that the global tasks of production in
planned and market economies are fundamentally different, and this is the foundation of the
rationale, which differ essentially in the methodological foundations of the assessment of
production efficiency.
The main task of a planned economy (maximally meeting the needs of society in essential
goods) set a specific goal for production - an increase in the volume of production, not paying
due attention to the issue of production efficiency, and often leading to falsification of reported
data to match the planned and actual results. The primary task of the market economy (the
production of goods needed by the consumer with the maximum profit for the manufacturer)
forces the manufacturer to be more attentive to efficiency issues, since its competitiveness
primarily depends on it. One of the determining factors of production efficiency is the efficient
use of resources, especially energy.
An important condition for the sustainable development of the innovation process in
industrial enterprises is the unity of the innovation activities of interrelated industries, aimed at
reducing all the energy used, as measures of various forms of motion of matter. Innovative
activity in industrial energy-intensive industries in modern conditions is due to the adoption of
complex and expensive management conditions [2]. Any processes occurring in technology and
nature, require energy. Therefore, a number of economists propose the use of energy as the basis
for evaluating production efficiency and its development. Innovative activity in industrial energy-
intensive industries is necessary as a means of reducing the consumption of energy consumed.
Therefore, this research examines energy-entropic methods for evaluating the efficiency of
production and management, as an effective method of managing innovation, mainly by
optimizing the use of energy consumed based on the achievements of science and technology.
2. LITERATURE REVIEW
Many foreign researchers have been engaged in the evaluation of the economic efficiency of
production and economy using various criteria, methods, and methods: Kalirajan [3],
Kuosmanen, & Kortelainen [4], Hyde [5], Ziyadin, S. [6], Ziyadin, S. [7], Watkins, M. [8],
Kolawole, & Ojo [9], Iwasaki [10], Murillo‐Zamorano [11], etc.

3. Energy-Entropy Model for Assessment of Economic System Management
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Definitions of the energy-entropic processes in Economics are quite a lot, they are given in
the research work of Haddad [12] “Thermodynamics: The unique universal science”. Haddad
defines an energy-entropic processes as the transitions of systems from one state to another,
which are accompanied by certain changes in the magnitude of the state parameters, which allows
mathematically accurately describe each process and estimate the magnitude of the change in
energy and entropy in it.
According to the first law of energy-entropy – the law of energy conservation, no material
system can develop or function without consuming energy △ , which is spent on doing work
, on changing the internal energy of system △ and on dissipating heat into the environment
. .
The more it dissipates, the energy degrades, the more the entropy (S) increases. This is
evidenced by the second law of energy-entropy - the law of entropy increase: real isolated systems
tend to spontaneously move from a less probable state to a more probable or from a more ordered
to a less ordered (in the absence of forces that prevent it), i.e. only grow. Thus, in any isolated
system, the entropy increases, while the negentropy decreases. Therefore, negentropy
characterizes the quality of energy, and the second law expresses the law of decreasing energy
levels. Therefore, a system capable of producing work is considered as a source of negentropy
(for example, a charged battery, etc.).
The third law of energy-entropy – the law of reducing the entropy of open systems with
progressive development - sounds like this: the entropy of open systems in the process of their
progressive development is always reduced due to energy consumption from external sources.
Thus, this law is, as it were, opposed to the second law, but does not contradict it, since it refers
not to spontaneously changing isolated systems, but to the systems over which innovative activity
is carried out.
The fourth law of energy-entropy, the law of the limiting development of material systems:
while improving, material systems (technical, etc.) reach the limit characteristic for each set of
external and internal conditions, which can be expressed by the maximum value of the
corresponding type of negentropy. This value is calculated, for example, from the coefficient of
performance; at the same time, the criteria can almost always be reduced to the ratio of either the
energy used to the total expended or the achieved growth of negentropy to the energy expended
(or negentropy), i.e. the negentropic energy utilization ratio.
Finally, the fifth law of energy-entropics is the law of preferential development, or the law of
competition: in each class of material systems, those with a given set of internal and external
conditions reach the maximum value of negentropy or maximum energy efficiency (specific
performance, durability, reliability, etc.).
Thus, the energy-entropy system is a macroscopic part of matter allocated for research.
3. METHODOLOGICAL FRAMEWORK
The authors, based on the above studies of the formation and development of innovative activities
of enterprises as a system and the laws of energy-entropics, reviewed the analyzed production,
revealed the cyclical nature of innovative development and suggested using the energy-entropy
balance approach to the management of innovative activities
An example of entropy [13] calculation (quantitative influence of entropic processes on
production) [14] in the case of two irreversible processes:
1. according to the linear law = ∑ , , = 1, , the flows are expressed as
= + ,
= + , (1)

4. Natalia Natocheeva, Ludmila Goloshchapova, Olga Veremeeva, Marianna Nazaeva and Victor Moroz
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Where, , are thermodynamic forces (disturbance);
2. for the entropy source in = ∑ = ∑ , we get the square-law form
= + + + . (2)
According to = ∑ = ∑ , > 0, the square-law form must be positive for all
values of and except for = = 0 when the entropy production is equal to zero (but
nothing changes in the system). According to [15] this requirement gives the following
inequalities:
> 0, > 0,
+ > 4 . (3)
Hence, coefficients k11, k22 are positive, whereas reciprocity coefficients , can be
both positive and negative but their values are limited by the condition (3).
For the general case, we will introduce the following notations:
= + " #,
= ,
" # = " #. (4)
Therefore and " # are symmetric and asymmetric parts of kinetic coefficients.
According to [16], the asymmetric part does not contribute to the production of entropy =
∑ = ∑ , and, hence:
= ∑ , ≥ 0, (5)
or in matrix representation:
= %
∗ ' ∗ ≥ 0, (6)
where, = (
)*…
),
-, %
= , … , are the force vector and transposed force vector; ' =
. / , ,
is a symmetric part of matrix '.
According to the theory of matrices of a special type [15], for any quadratic form there exists
such a linear transformation, which transforms this quadratic form into a quadratic form in new
variables with its subsequent transformation into a diagonal form. In particular, for the real
symmetric matrix ' there is such a real nonsingular matrix 0 that matrix ' = 0% ∗ ' ∗ 01 is
diagonal. The transformation to the main axes normalizes the given quadratic form:
%
' = 2%
'3 2 = ∑ 2 2 = ∑ 4 2 , (7)
where, 4 is the eigenvalue of matrix ' found as a solution to the characteristic equation
det ' − 4 = 0 for = 67…
7
7
…
7
…
………
7
7…
8; 2 = 2 , … , 2 are normal coordinates (correspond to the
eigenvalue); = 0 2, 0 = .9 / , ,
or = ∑ 9 :: ,
2:; '3 = 0%
∗ ' ∗ 0 or 2 : =
∑ ;,; , 9 9;:.
An additional transformation (normalization) 2 = </>?4 >, = 1, transforms formula (7)
to the canonical form:
%
' = ∑ @ < , (8)
Where coefficients

5. Energy-Entropy Model for Assessment of Economic System Management
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@ = A
+1, 4 > 0
−1, 4 < 0
0, 4 = 0.
For practical purposes, we recommend:
• an estimation relation
CD = 4 2 + 4 2 + ⋯ + 4 2
4F = G , H4 I, 4FJK = GLM , H4 I,
N ⟹ 4F . 2 + ⋯ + 2 / ≤ 'D
≤ 4FJK. 2 + ⋯ + 2 /
Or
4F ∑ 2 ≤ 'D ≤ 4FJK ∑ 2 .
Here ∑ 2 is the square of the length of the deviation vector 2: R 2R = ∑ 2 . As the linear
transformation does not distort the sizes, R 2R = ‖ ‖ is valid, i.e., the estimation is correct:
4F ∑ ≤ 'D ≤ 4FJK ∑ ; (9)
• For the comparative analysis the following fact [17] is used: For any two real,
symmetric forms %
T and %
' there is a real transformation such as =
∑ , , = 1, , or D = ' ∗ , = %
∗ D = %
∗ ' ∗ simultaneously
transforming the given forms to the canonical form.
4. RESULTS
The possibility to transform two quadratic forms to a canonical form enables comparison of two
single-type manufacturing departments at different enterprises or to compare products of different
technological levels produced at the same enterprise.
For non-closed systems the quadratic form is not necessarily positively defined. The
comparative analysis is based on the following theorem [17]: If at least one of the two real
quadratic forms is positively defined, there is a basis in which both forms will get a canonical
form. The results of the theorem can be applied to the matrices defined numerically. For example,
for a closed system one can use the model (the standard) for comparison of results and
conclusions of a real non-closed system. Comparing open systems with the standard, it is possible
to rank them according to the production efficiency and operating quality.
5. CONCLUSIONS
Today, innovations are introduced into various spheres of human activity, and nature of
innovation at each stage has its own specific features, which are very important for the manager,
as the current stage determines tasks and activities of the manager, and affects his methods and
tools [18]. According Abdrakhmanova, Mutanov, Mamykova, & Tukeyev, [19] informatization
of society involves radical social changes therefore high-quality expansion of the informatization
demands comprehensive accounting of a human factor, relevant there is a problem of adaption of
the person to life in the conditions of new information environment.
Entropic estimation of the state of production system parameters makes it possible to estimate
changes in parameters by a single relative indicator, and to synthesize such estimations into a
unified economic image of the current production situation. In the real production conditions at

6. Natalia Natocheeva, Ludmila Goloshchapova, Olga Veremeeva, Marianna Nazaeva and Victor Moroz
http://www.iaeme.com/IJMET/index.asp 1418 editor@iaeme.com
a certain moment of time, every value of the state of a controlled object corresponds to a certain
value of entropy [20].
As entropy is defined by a quadratic form, by knowing its value for a certain article one can
determine the efficiency of its production with respect to other articles. Based on the
mathematical statement on reduction of quadratic forms to the canonic form, the method
developed in the third chapter can be used for comparison of several single type productions.
More exact values of quadratic forms mean that this approach is justified mathematically and is
applicable for assessment of production systems.
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