[sodium.dioxid]

My textbook claims that the concept of entropy is needed to describe those reactions that are endothermic and yet occur spontaneously. For example, the spontaneous melting of ice in my hand is an endothermic process. However, couldn't we just explain whether or not something will occur by comparing the energy of the surrounding vs the energy of the system, and that there is a natural tendency for the energy of the two to equilibrate? In the case of melting ice, the surroundings simply has a higher energy than the system and when they come into contact, the surroundings experience energy loss and the system experiences energy gain.

[Araconan]

I'm also currently studying Thermodynamics, so I'll try and take a crack at this.

I'm not sure if I'm completely sold on your point regarding how there's a natural tendency for energy to equilibrate. Instead, I think it's more correct to state that there is a natural tendency for reactions to progress in the direction that allows for their free energy to be the lowest (which happens to be at equilibrium). Also, I'm not sure what you mean when you say "energy of the surroundings". Since "surroundings" are technically defined as anything other than the reaction itself, by definition, the surroundings would always have more energy than the system, which following your logic would imply that all endothermic reactions are spontaneous, which is incorrect. Are you instead referring to the energy of the reactions vs. the energy of the products?

You can mainly think of Entropy as a measurement of probability. Reactions will always occur in the direction that has the greatest probability of occurring, (an increase in entropy), and entropy was basically introduced to explain what force drives a reaction in a particular direction.

[manonemission]

Maybe this is oversimplified somehow, but I think of entropy and 'equilibration' as being due to a natural tendency for energy to migrate beyond its current state.  I.e. water molecules are in motion and thus must sooner or later reach another particle and make contact with it.  At the moment of contact, energy migrates between the particles and if one particle has less energy than another, it will retain more energy than it transfers away from itself.  I suppose that does sound like "a natural tendency to equilibrate."

It is also true that there is another natural tendency, i.e. to resist energy transfer.  Could this be called a fundamental insulating tendency?  Force causes acceleration, but it also causes dynamic harmony, which resists interruption.  The electrons organize into orbital patterns and resist deviating from those patterns.  More stable configurations resist energy transfers more.  Heat transferring to ice from tangential molecules melts or evaporates some of the ice without breaking the molecular bonds because those electrons are in a more stable pattern than the dipolar force interactions among the molecules.  So both melting and electrolysis of water can be called endothermic, but the molecular bonds are more insulated from absorbing system-energy than the molecules as wholes are. 

I see this as similar to the variability of absorption between black bodies and less absorptive substances.  Black bodies will absorb energy at any level, and could thus be called perfectly entropic.  Other substances, however, will only absorb energy at certain frequencies so they are more likely to reflect migrating energy as light or particle-motion.  Whether the equilibration between two particles occurs via light-energy transfer or particle-collision transfer thus has to do with how much their electron-configurations insulate against energy migrating to the form of electron-excitation, which I believe is also necessary for chemical bonding, no?

I hope my tone doesn't come across as too authoritative.  I'm really writing this tentatively to make sure I haven't overlooked issues that contradict my assumptions and conclusions.  Entropy mechanics are an interesting issue.