not change anything. Therefore, we will start numerating the laws of the Unified
Mechanics with the second law.
4.2.1 Second Law of Unified Mechanics Theory
Degradation of initial momentum of a body takes place according to the second law
of thermodynamics. The degradation rate is directly proportional to entropy generation rate along the path followed. Entropy generation can be mapped on a
nondimensional coordinate called Thermodynamic State Index (TSI), axis, Fig.
4.4, between zero and one. The second law of unified mechanics theory is nothing
but just a marriage of Newton’s second law and second law of thermodynamics in a
single equation. Thermodynamic State Index (Φ) is normalized nondimensional
form of the second law of thermodynamics; as a result, combination of the second
laws can be given by,
F 1 À Φ
ð
Þdt ¼ d mv
ð Þ
ð4:35Þ
Assuming a constant mass system
a ¼
F
m
1 À Φ
ð
Þ
ð4:36Þ
Combining the second law of Newton and thermodynamics requires the modification of Newtonian space-time coordinate system. A new axis must be added to be
able to define the thermodynamic state of the point (Fig. 4.4). As results, the motion
of any particle can be defined only in a five-dimensional space that has five linearly
independent axes. None of these axes can represent the information of other axes.
Y
Z
X
Time
Thermodynamic
State Index (TSI)
0
0.999
5 years old
100 years old
5 years old with
Stage4 cancer
100 years old
=
Fig. 4.4 Coordinate system of the unified mechanics theory
4.2 Laws of Unified Mechanics Theory
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