## 2 Materials and Methods
### Thermodynamic Characterization of SOM
Software in the TG-DSC is not well-designed yet for this purpose, and to measure the heat of combustion of SOM is necessary to export TG-DSC data to external auxiliary software to perform integrations, derivatives, and adjustments of baselines manually. For comparisons and applications of thermodynamic models, it is necessary to normalize the energy obtained in kJ g\({}^{-1}\) OM to the C content of the soil in C mole. That involves performing elemental analysis of the soil samples to relate the OM content obtained by the TG to the total C and/or organic C given by the elemental analysis [26]. To settle the correlation between C and SOM is essential for accurate normalizations since the existence of clay and/or carbonates may overlap with the OM content given by the TG measurements. That single correlation may optimize the most adequate value relating C to SOM in our samples to be used as the unit conversion factor. The high variety of soil properties could make this previous step essential for every soil, and it may be difficult to provide a general conversion factor. An example with some soils is shown in the results section of this paper. The soil samples were collected from the soil surface and at 5 cm of depth, representing Eutric vertisols and Podzols under oak mature forests collected in Ireland [26] and in the UK. Calculation of the enthalpy of combustion of SOM is possible for the reaction taking place in the DSC (and also in a bomb calorimeter), summarized as follows:  
\[\text{SOM(s)}+\text{xO}_{2}\text{(g)}=\text{yCO}_{2}\text{(g)}+\text{H}_{2} \text{O(g)}-\Delta_{\text{c}}\text{H}_{\text{SOM}} \tag{1}\]The TG-DSC analysis must be done under a flow of dry air, as reported [25]. \(\Delta_{\rm c}\)H\({}_{\rm SOM}\) is directly related to the degree of reduction of organic substrates by well-known relations [27; 28] involving the oxycloric quotient, Q\({}_{0}\), by the following general equation:  
\[\Delta_{\rm c}\rm H^{0}=Q_{0}\ \gamma_{\rm C} \tag{2}\]  
\(\Delta_{\rm c}\rm H^{0}\) is the enthalpy of combustion of any organic substrate at standard conditions; Q\({}_{0}\) is the oxycloric quotient representing the ratio between the enthalpy of combustion and the degree of reduction of C, \(\gamma_{\rm C}\), from organic substrates. Q\({}_{0}\) values vary in literature from \(-104\) to \(-118\) kJ mol\({}^{-1}\) degree of reduction\({}^{-1}\); all of them assigned to various authors [21]. They were determined for different organic substrates first and for microbial biomass later, yielding slopes in a similar range [21]. The reason for those differences comprises the structure of molecules which were considered in the latest corrections reported [28]. Recent works implementing these concepts [26] used the [PERSON] and Orbey value of \(-109\) kJ/C mol\({}^{-1}\) degree of reduction\({}^{-1}\)[28], but the reality is that the different values exhibited by the literature have not been applied for soils to compare results obtained by the different Q\({}_{0}\) values reported. [PERSON], and [PERSON] and Orbey's correlations [27; 28] give the Gibbs energy change for Equation (1), \(\Delta_{\rm c}\)G\({}_{\rm SOM}\). It would be interesting to apply both models to analyze and compare the resulting values for soil samples. The entropy change of Equation (1) is an interesting goal too, because of its involvement in the evolution of soil ecosystems [29]. It can be determined by models such as the one proposed by [PERSON] in 1999 [30]. It focuses on the application of the Hess law to microbial growth reactions where reactants and products are well-known. It is difficult to apply it when considering SOM as a reactant because we do not know the products for SOM biodecomposition in many cases. They can be assumed and summarized through different general concepts [31], but the reality is that we only can approach the formulation as done by the correlations between energy and the degree of reduction.