TdS ¼ K i ∇T
ð
Þ i þ R þ Mρ
À1
τ ij dε ij þ ϕdG þ γdA þ μdM
ð4:29Þ
As Klamecki (1984) points out this definition of entropy is very valuable since it
contains, or may be further generalized to contain, all the energy dissipation mechanisms in sliding bodies. Of course, there is nothing in the equation that limits it to
siding bodies only. Klamecki (1984) speculated that there are three regimes of
system behavior, which are of interest when the intent is to describe changes in
the system by the use of entropy generation. At thermodynamic equilibrium, the
system entropy is at maximum, and the change in entropy with time is zero. When
the system is not in equilibrium because of a continual supply of energy to it, it can
be near equilibrium or far from equilibrium state. Klamecki (1984) asserted that the
process occurring in the nonequilibrium states could be analyzed by studying the
entropy production in the system. The entropy created in the system is given by
TdS ¼ R þ Mρ
À1
τ ij dε ij þ ϕdG þ γdA þ μdM
ð4:30Þ
These terms have the general form of a thermodynamic force F, multiplied by a
corresponding flux, J. Then entropy production is
S ¼
X n
i¼1
F i J i
ð4:31Þ
where n is the number of internal entropy generation mechanisms. Entropy production rate is defined by
_
S ¼
dS
dt
¼
X n
i¼1
F i
dJ i
dt
þ J i
dF i
dt
ð4:32Þ
Here, Klamecki (1984) postulates that the first term in the summation represents
the entropy generation rate at far from the equilibrium state where thermodynamic
force does not change by time. The second term represents the entropy generation
near equilibrium. As a result, the summation can be summarized as follows:
_
S ¼ _
S J þ _
S F
ð4:33Þ
In near equilibrium, entropy production rate _
S F will continuously get smaller,
according to second law of thermodynamics. Thermodynamic forces change in such
a way that a stationary state of minimum rate of entropy generation results at
equilibrium, as stipulated by second law of thermodynamics.
_
S F ¼ 0
ð4:34Þ
126
4 Unified Mechanics Theory
ð
Þ i þ R þ Mρ
À1
τ ij dε ij þ ϕdG þ γdA þ μdM
ð4:29Þ
As Klamecki (1984) points out this definition of entropy is very valuable since it
contains, or may be further generalized to contain, all the energy dissipation mechanisms in sliding bodies. Of course, there is nothing in the equation that limits it to
siding bodies only. Klamecki (1984) speculated that there are three regimes of
system behavior, which are of interest when the intent is to describe changes in
the system by the use of entropy generation. At thermodynamic equilibrium, the
system entropy is at maximum, and the change in entropy with time is zero. When
the system is not in equilibrium because of a continual supply of energy to it, it can
be near equilibrium or far from equilibrium state. Klamecki (1984) asserted that the
process occurring in the nonequilibrium states could be analyzed by studying the
entropy production in the system. The entropy created in the system is given by
TdS ¼ R þ Mρ
À1
τ ij dε ij þ ϕdG þ γdA þ μdM
ð4:30Þ
These terms have the general form of a thermodynamic force F, multiplied by a
corresponding flux, J. Then entropy production is
S ¼
X n
i¼1
F i J i
ð4:31Þ
where n is the number of internal entropy generation mechanisms. Entropy production rate is defined by
_
S ¼
dS
dt
¼
X n
i¼1
F i
dJ i
dt
þ J i
dF i
dt
ð4:32Þ
Here, Klamecki (1984) postulates that the first term in the summation represents
the entropy generation rate at far from the equilibrium state where thermodynamic
force does not change by time. The second term represents the entropy generation
near equilibrium. As a result, the summation can be summarized as follows:
_
S ¼ _
S J þ _
S F
ð4:33Þ
In near equilibrium, entropy production rate _
S F will continuously get smaller,
according to second law of thermodynamics. Thermodynamic forces change in such
a way that a stationary state of minimum rate of entropy generation results at
equilibrium, as stipulated by second law of thermodynamics.
_
S F ¼ 0
ð4:34Þ
126
4 Unified Mechanics Theory