Stationary state is one of non-equilibrium states, and so entropy is generated
continuously in biological system. Change of entropy in internal system is
represented by d i S>0. All state functions do not depend on time in stationary state,
and it is formulated by
dS
dt ¼
d e S
dt þ
d i S
dt ¼ 0, where dS and d e S represent entropy change
of entire system and external environment, respectively. Continuous generation of
entropy in biological system is represented by
d i S
dt > 0s, and so results in
d e S
dt < 0. This
result indicates that negative flow of entropy compensates generation of entropy in
biological system for maintaining the stationary state.
Rate of entropy generation is defined as Φ ¼ T
d i S
st and then temporal change of Φ
as
dΦ
dt is considered. Biological system of open system has an internal term of
dΦ i
dt < 0
and an external term of
dΦ e
dt . Positive or negative sign of the external term is not
determined. Living organism is an open system, and flow of entropy is composed of
thermal flow and substantial flow. The flow of entropy is shown by j s ¼
q
T þ
P
i
j i s i .
When there is no thermal flow (q¼0), flow of entropy generated by substantial flow
and results in
P
i
j i s i , < 0. The equation indicates that entropy of imported substances is smaller than entropy of exported substances in stationary state.
1.3.1 Stationary State and Principle of Minimum Entropy
Production
From viewpoint of natural science, generation and maintenance of energy in biological system should be understood in frame of physics and chemistry. And
conversion of energy in biological system is determined by the second law of
thermodynamics. Highly ordered biological system is generated in
non-equilibrium system. I. Prigogine has analyzed the second law of thermodynamics from micro and macro viewpoint, and he has shown that ordered system is
generated in non-equilibrium state. The ordered system is in irreversible process
and generates entropy continuously and dissipates free energy. So, this system is
called as ‘dissipative structure’.
Ecological system on the earth is not in equilibrium system but in ‘dissipative
structure’ like biological system. Reversible process is going with fluctuation in
equilibrium state but never escape from equilibrium state. On the other hand,
‘dissipative structure’ exchanges energy and substances under a condition of
non-equilibrium state, and this exchange maintains dissipative structure’. Both
equilibrium state and stationary state do not change as time passes. However
stationary state produce entropy but equilibrium state does not produce entropy.
Stationary state is maintained by some fixed force (independent of time) of external
system. However, it is impossible to realize time-independent external system. So
stationary state is an ideal state in limited time scale. In other words, stationary state
has the minimum production of entropy under limited condition from external
14
1 Physics in the Origin of Life
continuously in biological system. Change of entropy in internal system is
represented by d i S>0. All state functions do not depend on time in stationary state,
and it is formulated by
dS
dt ¼
d e S
dt þ
d i S
dt ¼ 0, where dS and d e S represent entropy change
of entire system and external environment, respectively. Continuous generation of
entropy in biological system is represented by
d i S
dt > 0s, and so results in
d e S
dt < 0. This
result indicates that negative flow of entropy compensates generation of entropy in
biological system for maintaining the stationary state.
Rate of entropy generation is defined as Φ ¼ T
d i S
st and then temporal change of Φ
as
dΦ
dt is considered. Biological system of open system has an internal term of
dΦ i
dt < 0
and an external term of
dΦ e
dt . Positive or negative sign of the external term is not
determined. Living organism is an open system, and flow of entropy is composed of
thermal flow and substantial flow. The flow of entropy is shown by j s ¼
q
T þ
P
i
j i s i .
When there is no thermal flow (q¼0), flow of entropy generated by substantial flow
and results in
P
i
j i s i , < 0. The equation indicates that entropy of imported substances is smaller than entropy of exported substances in stationary state.
1.3.1 Stationary State and Principle of Minimum Entropy
Production
From viewpoint of natural science, generation and maintenance of energy in biological system should be understood in frame of physics and chemistry. And
conversion of energy in biological system is determined by the second law of
thermodynamics. Highly ordered biological system is generated in
non-equilibrium system. I. Prigogine has analyzed the second law of thermodynamics from micro and macro viewpoint, and he has shown that ordered system is
generated in non-equilibrium state. The ordered system is in irreversible process
and generates entropy continuously and dissipates free energy. So, this system is
called as ‘dissipative structure’.
Ecological system on the earth is not in equilibrium system but in ‘dissipative
structure’ like biological system. Reversible process is going with fluctuation in
equilibrium state but never escape from equilibrium state. On the other hand,
‘dissipative structure’ exchanges energy and substances under a condition of
non-equilibrium state, and this exchange maintains dissipative structure’. Both
equilibrium state and stationary state do not change as time passes. However
stationary state produce entropy but equilibrium state does not produce entropy.
Stationary state is maintained by some fixed force (independent of time) of external
system. However, it is impossible to realize time-independent external system. So
stationary state is an ideal state in limited time scale. In other words, stationary state
has the minimum production of entropy under limited condition from external
14
1 Physics in the Origin of Life