'The bigger the slope (in space), the faster (in time) the temperature changes at that point!' - Sorry but I'm not really reading you here. If the points around an 'atom' a symmetrically and equally far away when it comes to the point in question but are opposite in magnitude (i.e. imagine having a point with temperature 12 degrees Celsius which is surrounded by a neighboring points which have temperatures of 8 degrees and 16 degrees (so the delta is +4 and -4) then the temperature here will stay the same. The slope of the temperature field has nothing to do with this - unless maybe you're alluding to the slope of something else? I think I should have maybe explained this equation in terms of 'concavity' instead of using the methodology which I used - you can get a good grasp of this in this link: https://www.youtube.com/watch?v=b-LKPtGMdss
Thanks for taking the time to respond and analyze my comment! - The bigger the slope (in space), the faster (in time) the temperature changes at that point -
I have to confess that I got it wrong, indeed: the right side of the equation is a Laplacian. But, rather than describing an average in temperature, it describes the divergence of the temperature field.
