ENERGY I N ANIMAL ECOLOGY
79
An expression of the same form is used in the definition of the
statistical mechanical concept of entropy.
The statistical mechanical concept of entropy is in principle equivalent t o the thermodynamic concept of entropy and changes in entropy
are measurable for chemical systems at known pressures and temperatures by using the relation.
in which P is pressure, T absolute temperature, A V and A F are
changes in volume and free energy, A F is the change in energy level
of the system, defined aa Q - u’ where Q is the heat evolved during a
transformation and W is t’he work done.
Q
AS is defined as - or entropy change. The system is assumed t o be
T
thermodynamically isolated.
It would be very nice if we could, by suitable measurements, measure
the various terms in Eq. (11) and, thereby, utilize the full theoretical
power of thermodynamics in our analysis of ecological systems. The
second law of thermodynamics, which can be verbalized as follows,
“In an isolated system, the internal entropy is maximum when the
system is in thermodynamic equilibrium”, must be considered applicable in some sense t o ecological communities. Apart from other theoretical and operational difficulties, which we will discuss below, an
immediate problem arises from the fact that an ecological community
cannot in any sense be considered as thermodynamically isolated, nor
can any system containing a living organism 5e considered in thermodynamic equilibrium.
The equivalent law for a non-isolated steady state system is Prigogine’s theorem which has been stated as fcllows by Foster et al.
(1957) : “In an open system, the rate of internal entropy production,
which is always positive, is minimized when the system is in a steady
state.” An open system is defined by these authors as one which exchanges both energy and matter with the ambient universe. They,
then, made a theoretical analysis which is immediately germane t o the
problem of the relation between thermodynamics and ecology.
They considered an electronic circuit in which internal entropy
production is simply and directly proportional t o the heat production
or power dissipation by the resistance and is directly calculable from
Kirchhoff’s Laws. They find that for certain simple circuits the open
system second law of thermodynamics actually does hold.
However, if feedback occurs within the circuit, Prigogine’s theorem
does not necessarily hold. If the system is characterized by the presence
of interlocking feedback loops, the theorem only holds if arbitrary
79
An expression of the same form is used in the definition of the
statistical mechanical concept of entropy.
The statistical mechanical concept of entropy is in principle equivalent t o the thermodynamic concept of entropy and changes in entropy
are measurable for chemical systems at known pressures and temperatures by using the relation.
in which P is pressure, T absolute temperature, A V and A F are
changes in volume and free energy, A F is the change in energy level
of the system, defined aa Q - u’ where Q is the heat evolved during a
transformation and W is t’he work done.
Q
AS is defined as - or entropy change. The system is assumed t o be
T
thermodynamically isolated.
It would be very nice if we could, by suitable measurements, measure
the various terms in Eq. (11) and, thereby, utilize the full theoretical
power of thermodynamics in our analysis of ecological systems. The
second law of thermodynamics, which can be verbalized as follows,
“In an isolated system, the internal entropy is maximum when the
system is in thermodynamic equilibrium”, must be considered applicable in some sense t o ecological communities. Apart from other theoretical and operational difficulties, which we will discuss below, an
immediate problem arises from the fact that an ecological community
cannot in any sense be considered as thermodynamically isolated, nor
can any system containing a living organism 5e considered in thermodynamic equilibrium.
The equivalent law for a non-isolated steady state system is Prigogine’s theorem which has been stated as fcllows by Foster et al.
(1957) : “In an open system, the rate of internal entropy production,
which is always positive, is minimized when the system is in a steady
state.” An open system is defined by these authors as one which exchanges both energy and matter with the ambient universe. They,
then, made a theoretical analysis which is immediately germane t o the
problem of the relation between thermodynamics and ecology.
They considered an electronic circuit in which internal entropy
production is simply and directly proportional t o the heat production
or power dissipation by the resistance and is directly calculable from
Kirchhoff’s Laws. They find that for certain simple circuits the open
system second law of thermodynamics actually does hold.
However, if feedback occurs within the circuit, Prigogine’s theorem
does not necessarily hold. If the system is characterized by the presence
of interlocking feedback loops, the theorem only holds if arbitrary