Consider a system and its two end states, A and B. The preferred direction of any
spontaneous natural process (for instance, in the direction of A ! B) is determined
by the condition of positive entropy production. The entropy law asserts that entropy cannot be destroyed, but makes no claim with regard to how large entropy
production must be as long as it remains nonnegative. Significantly, a system
change between the same A ! B can take place under a perfect management for
achieving the reversibility limit with vanishing entropy production theoretically—
only a change of the nature beyond the limit is physically impossible. By setting the
limit to what is physically possible in an irreversible world, the second law suggested possibilities that had been hitherto unrecognized in a reversible dynamical
world. That insight was realized long ago by Poincaré
[These thermodynamic laws] can have only one significance, which is that there is a
property common to all possibilities; but in the deterministic hypothesis there is only a
single possibility, and the laws no longer have any meaning. In the indeterministic
hypothesis, on the other hand, they would have meaning, even if they were taken in an
absolute sense; they would appear as a limitation imposed upon freedom (Poincaré, 1913,
pp. 122–123 [26]).
The more interesting point in Poincaré’s comment on the limitation-of-possibilities
is not the limitation imposed on the freedom, but the existence of this freedom. This
freedom manifests in thermodynamic drive force that can be managed for a range of
event possibilities. The possibility and necessity of exercising management are put in
this way by Lotka, “The two fundamental laws of thermodynamics are, of course,
insufficient to determine the course of events in a physical system. They tell us that
certain things cannot happen, but they do not tell us what does happen” [27]. That is,
the mathematical expression of the two laws of thermodynamics is not in the form of
governing equations, which do determine what happens. For thermodynamic systems,
management or action, in addition to the mathematical expression of the two laws, is
what makes non-spontaneous events happen.
Poincaré’s “single possibility” is the spontaneous natural event (limit), one
reference limit of all possible A ! B processes. The other limit is the reversible
A ! B event. We consider the system in the context of a T 0 -environment-reservoir.
Let heat exchange of the spontaneous natural event between the
(fuel-and-equipment) system and the reservoir to Q spon , which is defined by convention here to be positive if the system gains heat from the reservoir and correspondingly negative if heat is released to the reservoir. Let heat exchange of the
corresponding reversible event between the system and the reservoir to be Q rev .
And let heat exchange (between the system and the reservoir) of an arbitrary real
process (among infinitely many possible A ! B processes) to Q. The first and
second laws infer the following corollary, the entropic drive corollary [28]:
An event of a system between two end states is characterized by the system-T 0 reservoir
heat exchange of the event. The useful range of possible events (called the Poincare range)
is defined by the spontaneous limit and the reversible limit, with the (system-T 0 reservoir)
8.3 The Entropic Drive Corollary
197
spontaneous natural process (for instance, in the direction of A ! B) is determined
by the condition of positive entropy production. The entropy law asserts that entropy cannot be destroyed, but makes no claim with regard to how large entropy
production must be as long as it remains nonnegative. Significantly, a system
change between the same A ! B can take place under a perfect management for
achieving the reversibility limit with vanishing entropy production theoretically—
only a change of the nature beyond the limit is physically impossible. By setting the
limit to what is physically possible in an irreversible world, the second law suggested possibilities that had been hitherto unrecognized in a reversible dynamical
world. That insight was realized long ago by Poincaré
[These thermodynamic laws] can have only one significance, which is that there is a
property common to all possibilities; but in the deterministic hypothesis there is only a
single possibility, and the laws no longer have any meaning. In the indeterministic
hypothesis, on the other hand, they would have meaning, even if they were taken in an
absolute sense; they would appear as a limitation imposed upon freedom (Poincaré, 1913,
pp. 122–123 [26]).
The more interesting point in Poincaré’s comment on the limitation-of-possibilities
is not the limitation imposed on the freedom, but the existence of this freedom. This
freedom manifests in thermodynamic drive force that can be managed for a range of
event possibilities. The possibility and necessity of exercising management are put in
this way by Lotka, “The two fundamental laws of thermodynamics are, of course,
insufficient to determine the course of events in a physical system. They tell us that
certain things cannot happen, but they do not tell us what does happen” [27]. That is,
the mathematical expression of the two laws of thermodynamics is not in the form of
governing equations, which do determine what happens. For thermodynamic systems,
management or action, in addition to the mathematical expression of the two laws, is
what makes non-spontaneous events happen.
Poincaré’s “single possibility” is the spontaneous natural event (limit), one
reference limit of all possible A ! B processes. The other limit is the reversible
A ! B event. We consider the system in the context of a T 0 -environment-reservoir.
Let heat exchange of the spontaneous natural event between the
(fuel-and-equipment) system and the reservoir to Q spon , which is defined by convention here to be positive if the system gains heat from the reservoir and correspondingly negative if heat is released to the reservoir. Let heat exchange of the
corresponding reversible event between the system and the reservoir to be Q rev .
And let heat exchange (between the system and the reservoir) of an arbitrary real
process (among infinitely many possible A ! B processes) to Q. The first and
second laws infer the following corollary, the entropic drive corollary [28]:
An event of a system between two end states is characterized by the system-T 0 reservoir
heat exchange of the event. The useful range of possible events (called the Poincare range)
is defined by the spontaneous limit and the reversible limit, with the (system-T 0 reservoir)
8.3 The Entropic Drive Corollary
197