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.