Thermodynamic interpretation of composting process using approximate integral functional

抄録

　Assuming that the composting process, which is a type of ecosystem, may be linked to an integral functional maximization problem, the author discusses how the temporal spatial distribution of state variables can be treated as an extremal problem. The object item of maximization is recognized as the net released exergy at each moment in the process.
　As composting is accompanied by bifurcations due to nonlinear temperature dependence of reaction rate, it is uncertain whether an exact integral functional exists that can precisely predict the temporal progress of the phenomenon. However, the fact that the maximization principle of the net released exergy at each moment holds is considered to support Jorgensen's theory that exergy can be regarded as a Lyapunov function of the process for periods under temporal stable conditions before and after bifurcation. The mathematical treatment herein is an approximation that assumes that temperature is the only dependent variable, provided that the other dependent variables—moisture content and oxygen concentration—are not restriction factors in the system progress.
　It is substantially difficult at this stage to obtain an exact integral functional considering the mutual dependence of temperature, moisture content, and oxygen concentration with biochemical reactions. If the permissible extent of the calculated results is not extremely narrow, there is a high possibility of obtaining an approximate integral functional and using it to formulate the maximization problem.