Enthalpy  Entropy  Gibbs Free Energy 


Enthalpy is the amount of heat energy transferred (heat absorbed or emitted) in a chemical process under constant pressure.  Entropy measures the amount of heat dispersed or transferred during a chemical process.  Gibbs Energy is also known as energy available to initiate a chemical process under constant pressure and temperature. 
It is expressed as a change in enthalpy (ΔH) because the total enthalpy (H) of a system cannot be measured directly.  Nature tends to form chaos than order — aging, decaying, rusting, etc. Usable energy is transformed to unusable energy when work is performed. Entropy is often described as a measure of randomness but this mustn’t be confused with random patterns or arrangements.Entropy is about heat. The change in entropy is expressed as ∆S. The higher energy dispersal means higher entropy.  Some reactions are spontaneous (eg. rusting). A spontaneous process happens by itself without any energy added to the system. A nonspontaneous process requires energy to be added to the system to kick off the chemical reaction.
∆G = ∆H — T•∆S∆G = Gibbs Free Energy ∆H = Change in Enthalpy T = Temperature in K ∆S = Change in Entropy 
ΔH > 0  ∆S > 0  ∆G < 0 
• Total energy of products greater than total energy of reactants.
• The process is exothermic. • Gives off heat. 
Entropy increases.  Process is spontaneous 
The relation [dS <0] looks like a typo. I think it should be [dG <0], neatly fitting beneath the explanation for Gibbs' Energy :).
Thank you!!