## 2 Materials and Methods
### Thermodynamics of the Soil Microbial Metabolism (SMM)  
Microorganisms decompose SOM by different biochemical paths and different electron acceptors [31]. Nevertheless, most of the studies focusing on SMM bioenergetics apply to the aerobic decomposition of SOM, where O\({}_{2}\) is the electron acceptor. The interest in characterizing SMM from a thermodynamic perspective is linked to the development of calorimeters that measure the heat released by SMM [32]. As the aerobic decomposition of SOM releases CO\({}_{2}\) too, calorimeters have been adapted to monitor the heat and CO\({}_{2}\) from SMM by different caloresiprometric procedures [33]. These studies for soils started at the beginning of this century, involving very recent findings [34; 35]. The concomitant measurements of heat and CO\({}_{2}\) have the advantage to yield the caloresiprometric ratio (CR) of SMM, a metabolic indicator providing additional information about the nature of substrates from SOM being decomposed during the caloresiprometric measurement [31; 36]. CR is a measure of the enthalpy of those substrates [26] and the microbial metabolic C-use efficiency, CUE [37].  
For the thermodynamic characterization of SMM, it is essential to link CR values to the enthalpy of the substrates [26; 31]. Assuming CR represents the enthalpy for substrates being metabolically decomposed, \(\Delta_{\rm r}\rm H_{SOM}\), it would be possible to yield the Gibbs energy change for microbial decomposition of SOM, \(\Delta_{\rm r}\rm G_{SOM}\), by the models developed for microbial metabolism [20; 27; 28]. Comparing \(\Delta_{\rm r}\rm G_{SOM}\) values with those from SOM combustion in Equation (1), \(\Delta_{\rm c}G_{\rm SOM}\), can shed light on microbial strategies to keep soil ecosystems far from equilibrium, an unexplored field. It is also not known how the \(\Delta_{\rm c}H_{\rm SOM}\) and \(\Delta_{\rm c}G_{\rm SOM}\) values may influence the soil microbial functions and soil microbial diversity. It would be possible to localize soils with SOM at more, or less, degree of reduction by their \(\Delta_{\rm c}H_{\rm SOM}\) and \(\Delta_{\rm c}G_{\rm SOM}\) values, to relate them to the complexity of the SOM macromolecule and to the properties of the soil microbial community on those locations in terms of soil microbial diversity and soil microbial metabolic diversity. There is no previous work to this respect and there is an example of it in the results section.  
The set of soil samples from different depths collected in oak mature forests were calorespirometrically characterized for aerobic decomposition of SOM by a microbial community at steady-state metabolism.  
The reaction for SOM biodecomposition in this case is summarized as follows:  
\[\rm{SOM(s)+O_{2}(g)=Products(s)+H_{2}O(l)+CO_{2}(g)-\Delta_{r}H_{\rm SOM}} \tag{4}\]  
where \(\Delta_{r}H_{\rm SOM}\) is directly determined by calorespirometry as the CR. The experimental procedure is well-explained by the literature [38]. \(\Delta_{r}H_{\rm SOM}\) gives the degree of reduction, \(\gamma_{r}\), of the substrates being metabolically decomposed [26]:  
\[\rm{CR-\Delta_{r}H_{\rm SOM}=\gamma_{r}/4\ (-455)\ kJmol^{-1}O_{2}} \tag{5}\]  
The Gibbs energy change for Equation (4), \(\Delta_{r}G_{\rm SOM}\), is given by the relations reported by [PERSON], and [PERSON].  
The entropy change is determined by adaptation of Equation (3) to Equation (4) at the temperature of the caloresipirometric measurement (298 K).