The authors present an innovative relationship between the earthquake hazard and the Second Law of Thermodynamics by using the Shannon entropy, H, as a indicator of the changes in the seismic activity of a region.

I recommend to accept it after the author incorporate the minor revisions (see attached document)

In the paper “Earthquake hazard characterization by using entropy: application to northern Chilean earthquakes” the authors discuss a statistical physics approach for the characterization of seismicity evolution and dynamics in Northern Chile. To this end, the authors use the relationship between the Gutenberg-Richter scaling relation and the Shannon entropy to demonstrate variations in entropy associated with the occurrence of strong earthquakes in this region. The manuscript is generally well-written and organized, the methodology is sound, and the results present some interest for the scientific community. Therefore, I recommend its publication after some minor revisions listed below.

1) In Equation 6 and so on, the upper limit of the integral, representing the interval of earthquake magnitudes, is infinity. However, there is a maximum magnitude up to which earthquakes occur. I would suggest substituting the infinity symbol with Mmax.

2) In Page 4, the annotation given first to the parameter n is “the number of earthquakes with magnitude M”, whereas later on “the cumulative number of earthquakes with a magnitude equal to or larger than M”. The annotation given to particular parameters should be consistent throughout the text.  

3) Equation 17 has also been derived by De Santis et al. (2011). Provide the appropriate references and/or discussion.

4) The authors use the MAXC method to estimate the magnitude of completeness (Mc) of their catalog. Woessner and Wiemer (BSSA, 2005) suggested that Mc calculated with this method should be corrected to +0.2 units of magnitude to give more robust estimation of the b-value. Did the authors consider this correction?    

5) As the authors discuss in Figure 9, the threshold magnitude (Mc in my previous comment) varies with depth. However, in their analysis of the entire catalog, they use a common threshold magnitude for all depth ranges. In addition, it is possible that Mc also varies with time, and it should be estimated in the temporal windows. The proper estimation of Mc (or M₀) is crucial for the determination of the b-value (see Eq. 18).

6) In Figure 1 show the position of the second largest region on the globe.

7) The authors mention the Gutenberg-Richter scaling relation in Fig.4, as well as in other figures (Fig.9). However, in these figures only the cumulative and discrete frequency-magnitude distribution is shown. Show also the Gutenberg-Richter relation and the associated a and b parameters. 

8) What do the colors indicate in Fig.6?