352
9 Bioenergetics
cyclic process, the net change in the entropy of the system and its environment must
not be negative. If the change is zero, this cyclic process is reversible.
If the system is closed, then δQ = 0, and any change in the system changing
it from state A to state B either preserves its entropy or the entropy increases.
Thus, following Classius, we have found that the one statement of the 2nd
Law of Thermodynamics, “heat never flows from a cold body to a hotter one
spontaneously,” can be used to prove the existence of an extensive thermodynamic
variable called the entropy and that the entropy of a closed system never decreases.
The spontaneous progression of a closed system from any state to an equilibrium
state cannot cause a decrease of its entropy. The equilibrium state must have a
maximum entropy under the constraints there are on the closed system. If the system
can change internally to a state of greater entropy, it will do so. 33
For example, if a part of the system could expand doing work while taking in
an equivalent amount of heat energy, it will happen, thereby increasing the total
entropy of the system.
As we indicated, life systems may be considered as thermodynamic systems,
even though there are some energy occupations of metastable molecules which
are highly excited. Thermodynamic considerations are possible for cellular entities
because water as a background solution is plentiful. Not a large portion of the
energetic macromolecules change state in observational times. The pressure and
temperature do not fluctuate significantly when measured over small regions of a
cell. In fact, these two intensive variables are nearly constant from one region to the
next. Metabolic processes, to good approximation, take place at fixed p and T .
Even though the entropy of a growing biological system decreases, life systems
do NOT violate the second law of thermodynamics. They are OPEN systems. As
such, they can drop in entropy, at the expense of their environment. The net change
in the entropy of a life system and its environment does not decrease. Building
a chicken from an egg, building proteins from amino acids, and making memory
all involve a decrease in entropy of the life system being described. While these
processes are occurring, there MUST be heat expelled to the outside. For example,
if this heat Q is released into an environment at a fixed temperature T E , the
entropy change of the environment will be S E = Q/T . If the life system has
correspondingly dropped in entropy by S L , then the drop in entropy in the life
system cannot be greater than Q/T .
With the new extensive quantity S characterizing a system, we can finally express
the heat into a system in terms of a path integral over quasi-static changes of the
system, since δQ = T dS. The changes in the energy of an open system is now
expressible as 34
33 But the time for any given process is not given by thermodynamics. Some processes may take
‘forever’.
34 Added work terms would be included if the system is in an electric field acting on electric
charges and dipoles, a magnetic field acting on magnetic dipoles, or has a bounding surface with
surface tension. They all can be put into the form f dX, where f is a generalized force, and dX a
9 Bioenergetics
cyclic process, the net change in the entropy of the system and its environment must
not be negative. If the change is zero, this cyclic process is reversible.
If the system is closed, then δQ = 0, and any change in the system changing
it from state A to state B either preserves its entropy or the entropy increases.
Thus, following Classius, we have found that the one statement of the 2nd
Law of Thermodynamics, “heat never flows from a cold body to a hotter one
spontaneously,” can be used to prove the existence of an extensive thermodynamic
variable called the entropy and that the entropy of a closed system never decreases.
The spontaneous progression of a closed system from any state to an equilibrium
state cannot cause a decrease of its entropy. The equilibrium state must have a
maximum entropy under the constraints there are on the closed system. If the system
can change internally to a state of greater entropy, it will do so. 33
For example, if a part of the system could expand doing work while taking in
an equivalent amount of heat energy, it will happen, thereby increasing the total
entropy of the system.
As we indicated, life systems may be considered as thermodynamic systems,
even though there are some energy occupations of metastable molecules which
are highly excited. Thermodynamic considerations are possible for cellular entities
because water as a background solution is plentiful. Not a large portion of the
energetic macromolecules change state in observational times. The pressure and
temperature do not fluctuate significantly when measured over small regions of a
cell. In fact, these two intensive variables are nearly constant from one region to the
next. Metabolic processes, to good approximation, take place at fixed p and T .
Even though the entropy of a growing biological system decreases, life systems
do NOT violate the second law of thermodynamics. They are OPEN systems. As
such, they can drop in entropy, at the expense of their environment. The net change
in the entropy of a life system and its environment does not decrease. Building
a chicken from an egg, building proteins from amino acids, and making memory
all involve a decrease in entropy of the life system being described. While these
processes are occurring, there MUST be heat expelled to the outside. For example,
if this heat Q is released into an environment at a fixed temperature T E , the
entropy change of the environment will be S E = Q/T . If the life system has
correspondingly dropped in entropy by S L , then the drop in entropy in the life
system cannot be greater than Q/T .
With the new extensive quantity S characterizing a system, we can finally express
the heat into a system in terms of a path integral over quasi-static changes of the
system, since δQ = T dS. The changes in the energy of an open system is now
expressible as 34
33 But the time for any given process is not given by thermodynamics. Some processes may take
‘forever’.
34 Added work terms would be included if the system is in an electric field acting on electric
charges and dipoles, a magnetic field acting on magnetic dipoles, or has a bounding surface with
surface tension. They all can be put into the form f dX, where f is a generalized force, and dX a