2. THERMODYNAMICS OF LIVING SYSTEMS
33
example, consider the case of diffusion. Let us suppose we have a container which is divided into a large section filled with water and a
smaller section to the left filled with a dye solution. A partition separates the two sections thus preventing the two liquids from mixing. Suppose now that the partition is removed. After a sufficient time interval,
one observes that the solution has become uniformly colored.
Diffusion does not necessarily arise as a result of interaction between
molecules such that the dye molecules are forced away from a crowded
region. To a first approximation, every dye molecule behaves independently of the others. Diffusion is a statistical phenomenon. Following
the example of Schrödinger (3), if the container is imagined to be cut
up into thin slices we have the following situation: at the time when
the partition is lifted out at the left side there is a great concentration
of dye molecules. Each molecule is being jostled by its neighbors until
it acquires sufficient energy to allow it to jump into an empty site or
"hole." Now the probability that the molecule will jump to the left is
just the same as that it will jump to the right, but at the instantaneous
border which exists just as the partition is removed, more dye molecules are in the thin slice to the left. Thus, more dye molecules will
jump to the right. This process will continue until there is a uniform
distribution of the dye molecules throughout the solvent. Now the Second Law states that in such a system there will be a drift toward the
most random state, which in this case results after the dye molecules
have distributed themselves equally throughout the solution.
If we consider one individual dye molecule, we see that the probability of its jumping in any direction is the same. Thus, the Second Law
applied to an individual molecule has no meaning, for in this case any
distinction between disordered energy, i.e., heat, and ordered energy,
i.e., work, disappears.
Now suppose we insert the partition back into its original position.
Furthermore, suppose we equip the partition with a molecular gate
which is attended by a Maxwell demon. This creature, invented by the
famous physicist, Clerk Maxwell, has the remarkable faculty of being
able to discriminate between solvent molecules and dye molecules. The
demon operates the gate in such a manner as to permit only colored
molecules to pass to the left while solvent molecules are allowed to
pass only to the right. After a while, one would find all the colored molecules completely separated from the solvent molecules and a return to
the original condition results. This change, of course, is associated with
a decrease in entropy. Helmholtz was the first to raise a serious
scientific question along these lines. He inquired whether microorganisms may not have the ability of choice attributed to the hypothetical
33
example, consider the case of diffusion. Let us suppose we have a container which is divided into a large section filled with water and a
smaller section to the left filled with a dye solution. A partition separates the two sections thus preventing the two liquids from mixing. Suppose now that the partition is removed. After a sufficient time interval,
one observes that the solution has become uniformly colored.
Diffusion does not necessarily arise as a result of interaction between
molecules such that the dye molecules are forced away from a crowded
region. To a first approximation, every dye molecule behaves independently of the others. Diffusion is a statistical phenomenon. Following
the example of Schrödinger (3), if the container is imagined to be cut
up into thin slices we have the following situation: at the time when
the partition is lifted out at the left side there is a great concentration
of dye molecules. Each molecule is being jostled by its neighbors until
it acquires sufficient energy to allow it to jump into an empty site or
"hole." Now the probability that the molecule will jump to the left is
just the same as that it will jump to the right, but at the instantaneous
border which exists just as the partition is removed, more dye molecules are in the thin slice to the left. Thus, more dye molecules will
jump to the right. This process will continue until there is a uniform
distribution of the dye molecules throughout the solvent. Now the Second Law states that in such a system there will be a drift toward the
most random state, which in this case results after the dye molecules
have distributed themselves equally throughout the solution.
If we consider one individual dye molecule, we see that the probability of its jumping in any direction is the same. Thus, the Second Law
applied to an individual molecule has no meaning, for in this case any
distinction between disordered energy, i.e., heat, and ordered energy,
i.e., work, disappears.
Now suppose we insert the partition back into its original position.
Furthermore, suppose we equip the partition with a molecular gate
which is attended by a Maxwell demon. This creature, invented by the
famous physicist, Clerk Maxwell, has the remarkable faculty of being
able to discriminate between solvent molecules and dye molecules. The
demon operates the gate in such a manner as to permit only colored
molecules to pass to the left while solvent molecules are allowed to
pass only to the right. After a while, one would find all the colored molecules completely separated from the solvent molecules and a return to
the original condition results. This change, of course, is associated with
a decrease in entropy. Helmholtz was the first to raise a serious
scientific question along these lines. He inquired whether microorganisms may not have the ability of choice attributed to the hypothetical