Spontaneous changes
Because of matter and energy input, the growth and development of a
plant community should be in principle a natural process characterized
by spontaneous increases in its total biomass quantityC T and total number of plant species N .
The enthalpy H , Gibbs free energy G and entropy Sof a plant community are state functions all positively related toC T and N . Their increments, △H ,
△G and △S should be greater than zero subject to
△C T > 0 and △N >
0. Such changes shown by the experimental data in Table 1 thus followed
the 1st law of thermodynamics.
In contrast, the observed decrease in f/C T due to
increase in s/C T with increasing N (Table
1) obeys the 2nd law of thermodynamics that the
spontaneous change in the state of a system is an irreversible process
towards the direction of decrease in its intensity factor (Engel &
Reid, 2006). For a given system, ln(N ) and
ln(N m) are intensity factors related to the
average chemical potential μ , weighted standard chemical
potential μ 0 and average mass ratio x ,
respectively, by
∂f /∂C T =
∂h /∂C T -∂s m/∂C T = μ /(RT) =μ 0/(RT) - ln(1/x ) =
ln(N m) - ln(N ) (10)
(Eq. 25 in the theoretical section). Given temperature T ,
ln(N m) is a constant while increasing Nwill reduce x since x = 1/N . We shall have
△x < 0 and △μ < 0 as long as △N> 0, indicating that the change of an ecosystem is
essentially a process of species enrichment that leads to the decease in
its intensity factor μ .
The observed changes in s /C T andf /C T (Table 1) also obeys the
3rd law of thermodynamics regarding the principle of
entropy increase (Engel & Reid, 2006). As been discussed in the
previous paper, there can be two spontaneous changes related to entropy
increase, of which one is increasing s with increasing Nand the other one is increasing s towardss m at a given N . The general trend of
increasing s with increasing N is clearly demonstrated by
the positive correlation between s/C T and
ln(N ) in Fig. 3. The decrease in the mass ratio of the
transplanted species with increasing N illustrated in Fig. 1a
shows the potential trend of increasing s towardss m. The increase in the contribution of new
species naturally geminated in the plot to the total biomass quantityC T reduced the contribution ratio of the dominant
species, which in turn reduced the difference between the peakx i and average x . In accordance with the
maximum entropy theorem, s = s m atx i = x j = x =
1/N , s will get closer to s m at
higher N levels subject to the constraint
∑x i =1.
The fact that increasing N is the essential cause for △μ< 0 makes △N > 0 a useful indicator for
judging the spontaneity of an ecological process as it is technically
convenient to observe the change in N in the field. The inhabited
species at a habitat will not disappear without a specific cause and
thus △N < 0 is an indicator for an unnatural process,
or a warning signal of damage (e.g., mining). If the number of species
of an ecosystem remains unchanged, namely, △N = 0, it indicates
that the ecosystem gets closer to an equilibrium with its surroundings
(similar to that in Plot III). Since the basic trend holds in general
with no specific constraints, the criterion △N > 0
should be a valid index for determining the direction of spontaneous
changes for all open thermodynamic systems with continuous input of
matter and energy.