As far as the first anonymous referee is concerned I have nothing to say as he recommends publication of my paper

To the second referee, Valerio Lucarini, my answers to his remarks are 

Line 26 - reaction-diffusion systems - please tell me which you consider the relevant references to add to the bibliography

Line 52 - local equilibrium - I will add the reference to Ghil and Lucarini 2020

where local equilibrium is not mentioned explicitely but is implied in several discussions

Line 102 - $F_{0}$ is the equilibrium free energy which is different for different systems 

Line 119 - non--equilibrium is due to both the external field and the boundary conditions

Line 124 - the chemical potential in most of the models considered describes the interaction with the external reservoirs according to eq. (7)

Line 146 - the quantity $\epsilon^{-d}$ is extensive in space. A factor extensive in time appears in fluctuations of time averaged quantities.

Line 169 - this formulation represents at the mesoscopic level a form of detailed balance in non--equilibrium

Line 180 - I will add the definition of the Lagrangian

Line 188 - I will add a reference 

Line 202 - this is the energy dissipated by the fluctuation, not the total dissipated energy 

Line 224 - to which intermediate points and constraints are you referring?

Line 235 -  Summable with respect to space variables. I will add a comment on the analogy with critical phenomena

Line 241 - I will add a reference

Line 261 - The effect of long range correlations is that local thermodynamic variables are not independent at macroscopic distances

Line 294 - no, Q is the amount of particles through the origin which in an interval of time t for a diffusion process is of the order of square root of t. 

Line 345 - ok. Which references would you like to be mentioned, those of Line 26 ?