mechanothermodynamics—a generalized physical discipline—is possible by
constructing a bridge between Newtonian mechanics and thermodynamics. The
entropy is the bridge between Thermodynamics and Mechanics.” The first and
the second principles of mechanothermodynamics were presented. They
formulated foundation of the general theory of degradation evolution of
mechanothermodynamic systems for
• Energy theory of limiting states
• Energy theory of damage
• Foundations of the theory of electrochemical damage”
They provided mathematical fundamentals of the theory of interaction between
damage caused by loads of different nature (mechanical, thermodynamic, etc.).
Authors proposed a single function for critical damage (limiting) states of metals
and polymer materials operating in different conditions. The analysis of 136 laboratory
experiment results showed that this single logarithmic function is fundamental: it is
valid for low, average, and high-strength pure metals, alloys, and polymers over a wide
range of temperatures of medium (from helium temperature to 0.8 TS, where TS is the
material melting temperature) and mechanical stresses (up to the strength limit for
single static loading) while the fatigue life was of the order of 106–108 cycles.
Mechanothermodynamics uses the same idea as unified mechanics theory in
order to unify Newtonian mechanics and thermodynamics, that is, using entropy
as a bridge to connect Newtonian mechanics and thermodynamics, which was first
published in Basaran and Yan (1998). Sosnovskiy and Sherbakov (2015, 2016) used
a logarithmic function for evolution of degradation; it is not clear why they do not
use Boltzmann equation, since their logarithmic function can be obtained directly
from Boltzmann equation. The term tribo-fatigue-entropy in their work refers to
entropy generation in tribology [which is their focus] and fatigue process. They
surmise that if an analogy between light and strain energy is justified, then strain
energy absorption law may be similar to Bouger’s light absorption law. This law,
which is also exponential, becomes basis for their degradation function formulation.
Haddad (2017) published probably the most comprehensive review of the history
of thermodynamics from its classical to its postmodern forms. Haddad et al. (2005)
and Haddad (2019) also provided general systems theory framework for
thermodynamics which attempts to harmonize thermodynamics with classical Newtonian mechanics. The main idea used by Haddad (2019) to unify mechanics and
thermodynamics is attributed to Basaran and Yan (1998). Haddad stated that, “The
dynamical system notions of entropy proposed Haddad (2005, 2019), Basaran and
Yan (1998), Basaran and Nie (2004), Sosnovskiy and Sherbakov (2016) involving
an analytical description of an objective property of matter can potentially offer a
conceptual advantage over the subjective quantum expressions for entropy proposed
in the literature (e.g., Daróczy entropy, Hartley entropy, Rényi entropy, von Neumann entropy, infinite-norm entropy) involving a measure of information. An even
more important benefit of the dynamical systems representation of thermodynamics
is the potential for developing a unified classical and quantum theory that
130
4 Unified Mechanics Theory
constructing a bridge between Newtonian mechanics and thermodynamics. The
entropy is the bridge between Thermodynamics and Mechanics.” The first and
the second principles of mechanothermodynamics were presented. They
formulated foundation of the general theory of degradation evolution of
mechanothermodynamic systems for
• Energy theory of limiting states
• Energy theory of damage
• Foundations of the theory of electrochemical damage”
They provided mathematical fundamentals of the theory of interaction between
damage caused by loads of different nature (mechanical, thermodynamic, etc.).
Authors proposed a single function for critical damage (limiting) states of metals
and polymer materials operating in different conditions. The analysis of 136 laboratory
experiment results showed that this single logarithmic function is fundamental: it is
valid for low, average, and high-strength pure metals, alloys, and polymers over a wide
range of temperatures of medium (from helium temperature to 0.8 TS, where TS is the
material melting temperature) and mechanical stresses (up to the strength limit for
single static loading) while the fatigue life was of the order of 106–108 cycles.
Mechanothermodynamics uses the same idea as unified mechanics theory in
order to unify Newtonian mechanics and thermodynamics, that is, using entropy
as a bridge to connect Newtonian mechanics and thermodynamics, which was first
published in Basaran and Yan (1998). Sosnovskiy and Sherbakov (2015, 2016) used
a logarithmic function for evolution of degradation; it is not clear why they do not
use Boltzmann equation, since their logarithmic function can be obtained directly
from Boltzmann equation. The term tribo-fatigue-entropy in their work refers to
entropy generation in tribology [which is their focus] and fatigue process. They
surmise that if an analogy between light and strain energy is justified, then strain
energy absorption law may be similar to Bouger’s light absorption law. This law,
which is also exponential, becomes basis for their degradation function formulation.
Haddad (2017) published probably the most comprehensive review of the history
of thermodynamics from its classical to its postmodern forms. Haddad et al. (2005)
and Haddad (2019) also provided general systems theory framework for
thermodynamics which attempts to harmonize thermodynamics with classical Newtonian mechanics. The main idea used by Haddad (2019) to unify mechanics and
thermodynamics is attributed to Basaran and Yan (1998). Haddad stated that, “The
dynamical system notions of entropy proposed Haddad (2005, 2019), Basaran and
Yan (1998), Basaran and Nie (2004), Sosnovskiy and Sherbakov (2016) involving
an analytical description of an objective property of matter can potentially offer a
conceptual advantage over the subjective quantum expressions for entropy proposed
in the literature (e.g., Daróczy entropy, Hartley entropy, Rényi entropy, von Neumann entropy, infinite-norm entropy) involving a measure of information. An even
more important benefit of the dynamical systems representation of thermodynamics
is the potential for developing a unified classical and quantum theory that
130
4 Unified Mechanics Theory