## 2 Materials and Methods
### Methodology
It is also significant that the entropy change can be determined without detailed information on the process because entropy is a state function defined from the equilibrium state. Therefore, entropy change is a useful indicator for assessing the sustainability of complex natural systems, such as deltas [18]. The delta thermodynamic system is complex because it integrates river flow and marine energy composed of thermal, kinetic (waves and currents), and chemical (mixing of waters of different salinity gradients) energy. Therefore, assessing the self-organized delta distributions of water, sediment, and nutrients is difficult. The entropy change of the open natural system, dSystem, is composed of the entropy exchange with the environment, dS\({}_{\text{e}}\), and the internal entropy change, dS\({}_{\text{i}}\):  
\[\text{dS}_{\text{system}}=\text{dS}_{\text{e}}+\text{dS}_{\text{i}}. \tag{1}\]  
Differentiating this equation with respect to time gives the speed of change in the system entropy, dS/dt, which is equal to the speed of change in entropy between the system and the environment plus the system, and the speed of entropy production inside the system:  
\[\text{dS}_{\text{system}}/\text{dt}=\text{dS}_{\text{e}}/\text{dt}+\text{dS} _{\text{i}}/\text{dt}. \tag{2}\]  
The entropy exchange with the environment, dS\({}_{\text{e}}/\text{dt}\), which considers the process of energy exchange with the environment, can be positive or negative; however, dS\({}_{\text{i}}/\text{dt}\) can only be positive. This implies that the general entropy of a natural system can increase or decrease. However, the entropy of an open system decreases at the expense of the associated processes that produce positive entropy in other parts of the environment. Inthe open system study flow condition, the entropy change of a system is theoretically zero, and the system is sustainable, \(\Delta\mathrm{S_{System}}=0\). However, a characteristic of natural systems and organisms is that the system is in near-perfect order or a quasi-static state, and the system entropy has a minimal positive value. The minimization of entropy generation in man-made systems can be accomplished by designing the operating conditions. In a natural system, it occurs by capturing energy and matter from the environment to overcome the internal entropy increase. Therefore, the value of entropy corresponds to the entropies of the real system at a certain time and can be determined only by the set of local variables characterizing the state of the system. Climate and sea-level change affect the potential energy and entropy or sustainability of river systems--that is, their vulnerability--because entropy (uncertainty, disorder) and vulnerability are interrelated. The more disordered the system and the higher the entropy, the less energy is available for the system to work. Disorder--that is, the system equilibrium change--is transferred to the river's hydomorphology and ecosystems and changes the availability of WEF resources such that the system or delta gradually produces a new, less efficient biophysical environment. This reduces the availability of WEF resources for ecosystems and human society and endangers the biophysical economy and sustainable livelihoods. The effects of changes in energy and sediment supply in river basins, MSL rise, and seawater energy on deltas are multifaceted and complicated when it comes to simulations and future projections under variable climatic regimes. However, the equilibrium states of delta hydomorphology can be approximated using the following equation [18]:  
\[\mathrm{Q_{river}\cdot f_{r}=R\cdot A_{delta},} \tag{3}\]  
where \(\mathrm{Q_{river}\ (m^{3}/yr)}\) is the fluvial sediment supply by the river that is retained at the delta (\(\mathrm{f_{r}}\) between 0 and 1), \(R\ (m/yr)\) is the rate of MSL rise, and \(A\ (m^{2})\) is the surface area of the delta as the sum of the delta topset area \(\mathrm{A_{topset}\ (m^{2})}\) and foreset area \(\mathrm{A_{forest}\ (m^{2})}\).