9.25 On the Evolution of Driven Systems
415
producing an internal release of the stored energies, and eventually becoming one
temperature and consisting of constituent molecules with long-time stabilities and
distributed in energy states according to Boltzmann.
In general no matter how far from equilibrium a system might be, the concept
of energy conservation still applies, and the entropy of any macro subsystem
within the open system can still be calculated, in principle, through its statistical
measure. The temperature of a subsystem, i.e. the inverse of rate at which the
internal energy of that subsystem gains entropy, makes sense if its fluctuations
are significantly smaller than its value. Such fluctuations tend to be small if the
macro subsystems are solutions which can easily dissipate heat, such as subsystems
in proximity or containing liquid water (a solvent with an especially high specific
heat). The evolution of any such open subsystem follows microscopic laws of nature.
Moreover, typically after the thermodynamic relaxation time for the solvent, τ s , the
subsystem will be most likely found in those quasi-stable states which have longer
lifetimes than τ s and that have been built from prior natural and statistical sampling
of the possible structures.
A special case of an open system is one through which energy, perhaps in a
variety of forms, consistently or periodically flows through the system. These are
called ‘driven systems’. 74
If the energy flow is steady, then the phrase, ‘steadily driven system’ applies.
The system accepts energy from an external source and dissipates the energy into
the environment. The system can be realized by a mixture of particles capable
of taking up energy and transforming that energy into kinetic motion, excited
internal states, internal transport processes, and possibly into external work. Now
imagine that among those possible excited states are some that are quasi-stable.
The concentration of these states, if initially low, can build up. Moreover, some
of these quasi-stable states may, by chance, be capable of absorbing the incoming
energy more effectively than a system without such states. For example, a molecule
might form which resonates at an incoming photon frequency. These more capable
molecules will then be more likely to form, and their concentration will increase
with time, provided there is sufficient concentration of their constituents.
On top of the ordering process that produces molecules which are efficient at
absorbing the incoming energy, some of these molecules may act as intermediaries
to other secondary ordered structures. In effect, they act to lower the energy
barrier which had made the secondary structures unlikely, but are now more easily
accessible. This is the behavior of a catalyst. Again, the most likely secondary
structures will be those that are both more easily produced and that benefit from
being relatively more stable. The system will undergo a macroscopic change when
catalysts drive a large quantity of reactants toward their resultants.
74 Harold J. Morowitz emphasized that spontaneous order production occurs when a sufficiently
complex open system has an energy flow through it. See his book, Energy Flow in Biology, [Acad
Press] (1968).
415
producing an internal release of the stored energies, and eventually becoming one
temperature and consisting of constituent molecules with long-time stabilities and
distributed in energy states according to Boltzmann.
In general no matter how far from equilibrium a system might be, the concept
of energy conservation still applies, and the entropy of any macro subsystem
within the open system can still be calculated, in principle, through its statistical
measure. The temperature of a subsystem, i.e. the inverse of rate at which the
internal energy of that subsystem gains entropy, makes sense if its fluctuations
are significantly smaller than its value. Such fluctuations tend to be small if the
macro subsystems are solutions which can easily dissipate heat, such as subsystems
in proximity or containing liquid water (a solvent with an especially high specific
heat). The evolution of any such open subsystem follows microscopic laws of nature.
Moreover, typically after the thermodynamic relaxation time for the solvent, τ s , the
subsystem will be most likely found in those quasi-stable states which have longer
lifetimes than τ s and that have been built from prior natural and statistical sampling
of the possible structures.
A special case of an open system is one through which energy, perhaps in a
variety of forms, consistently or periodically flows through the system. These are
called ‘driven systems’. 74
If the energy flow is steady, then the phrase, ‘steadily driven system’ applies.
The system accepts energy from an external source and dissipates the energy into
the environment. The system can be realized by a mixture of particles capable
of taking up energy and transforming that energy into kinetic motion, excited
internal states, internal transport processes, and possibly into external work. Now
imagine that among those possible excited states are some that are quasi-stable.
The concentration of these states, if initially low, can build up. Moreover, some
of these quasi-stable states may, by chance, be capable of absorbing the incoming
energy more effectively than a system without such states. For example, a molecule
might form which resonates at an incoming photon frequency. These more capable
molecules will then be more likely to form, and their concentration will increase
with time, provided there is sufficient concentration of their constituents.
On top of the ordering process that produces molecules which are efficient at
absorbing the incoming energy, some of these molecules may act as intermediaries
to other secondary ordered structures. In effect, they act to lower the energy
barrier which had made the secondary structures unlikely, but are now more easily
accessible. This is the behavior of a catalyst. Again, the most likely secondary
structures will be those that are both more easily produced and that benefit from
being relatively more stable. The system will undergo a macroscopic change when
catalysts drive a large quantity of reactants toward their resultants.
74 Harold J. Morowitz emphasized that spontaneous order production occurs when a sufficiently
complex open system has an energy flow through it. See his book, Energy Flow in Biology, [Acad
Press] (1968).