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The way I understand the law, any process is implausible if the total entropy of the universe does not increase. Why is "Spontaneous" even a part of the wording, what does it mean?

Is it perhaps a part of the probabilistic theory of thermodynamics, in which it is not "impossible" for heat to flow from cold to hot, simply very very unlikely?

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  • $\begingroup$ Spontaneous means that the process doesn't need an external source of energy - like light and so - to occur. Also, it gives a direction to the universe "process" because there isn't any external source of energy, so the universe progress in the direction of increasing entropy. But maybe I am misunderstanding what you say.. $\endgroup$
    – user43021
    Aug 20, 2017 at 21:17
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    $\begingroup$ Please provide the statement of the second law that you're considering---there are many formulations of the second law, and (at least to me) it's not clear which one you're referring to. $\endgroup$ Aug 20, 2017 at 21:22
  • $\begingroup$ The phrasing i am referring to is: "In a spontaneous process, the entropy of the Universe increases." Taken from Keeler and Wothers' "Why Chemical reactions happen" page 8, although i am sure i have seen it otherwhere as well. $\endgroup$
    – Adroit
    Aug 21, 2017 at 4:39

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In chemical thermodynamics we are interested in the amount of work that can be done by a reaction as it proceeds towards equilibrium and whether a reaction will spontaneously proceed towards products or, if not, how much work is needed to bring it about. Spontaneous is used because experimentally reactions and processes occur without us having to do anything to bring them about, and this needed an explanation.

The second law can be stated as$^1$ 'Spontaneous changes are those which, if carried out under the proper conditions can be made to do work. If carried out reversibly they yield the maximum amount of work. In natural processes the maximum amount of work is never obtained.' This is also a general definition of equilibrium. A shorter definition of the second law is 'heat does not spontaneously flow from from a cold to a hot body'.

If there are differences in intensive properties then a spontaneous change is always that which eliminates the difference. Thus if there is a (perfect) piston with different pressures on either side, it will move to equalise the pressure. Similarly if there is a temperature difference between two bodies in contact with one another then 'heat flows' from the warmer to the colder. Similarly, a concentration difference in a solution will equalise. However, this cannot be used to predict the direction of a chemical reaction in which there may already be constant pressure, temperature or concentrations.

In a purely mechanical system, the direction of spontaneous change seems obvious and is one in which the potential energy is lowered to a minimum. It was thought at one time that the same would apply to chemical systems, i.e that the direction of spontaneous change was one that minimises the heat content of the system. But experiment shows that this is not the case, there are, for example, spontaneous endothermic reactions$^2$, so that another criteria is needed to predict the direction of a spontaneous reaction. This means understanding why for example, a gas expands to fill a container even though no loss of energy occurs on doing this. The missing idea is the entropy$^3$.

It used to be thought, before the second law was properly understood, that the maxiumum work a chemical reaction could do was to be found by converting all the heat of reaction into work. This was not bourne out by experiment and it is the free energy $\Delta G$ that gives the maxmum amount of work. Gibbs was the first to understood that the maximum amount of work is given by the first law unless some heat is taken in or given out to the surroundings. Thus the work done may be greater than the heat of reaction.

The second law requires that there be an increase in entropy during any actual process. Thus $dS_{sys} + dS_{surr} \ge 0$ for the system and surroundings. The sum of the two entropy production processes is always a positive quantity, but which can be zero in the case of a reversible process.

(Your speculation about statistical mechanics is partly correct, it is possible for entropy to 'run backwards' if only a very small number of molecules is considered and then only for a very short time. In 'normal' lab chemistry the number of molecules involved is vast say, $10^{18}$ so deviations from the average are minute.)

$^1 $ E. B. Smith, 'Basic Chemical Thermodynamics'.

$^2$ e.g. $\ce{Ba(OH)2(8H2O)_{(s)} + NH4SCN_{(s)} +heat \rightarrow Ba(SCN)2 + 2NH3 + 10H2O}$

$^3 $ The second law is needed because the first law offers too much latitude compared to experimental observations; by the first law heat could spontaneously flow from a cold to a hot body or a broken glass could spontaneously reform itself.

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Refer to Wikipedia. Please note that your understanding (If dS/dt isn't positive...) is tautological. That is (as far as we know), our Universe requires dS/dt to be positive (or perhaps I should say we've never seen otherwise). The 2nd Law is most useful for nearly perfectly isolated systems and systems near (or, arguably, at) equilibrium. "Spontaneous" refers to time-forward processes in systems which are not perturbed (by outside events/forces). Our laws of quantum mechanics do not distinguish between positive and negative time. Supposedly, any event which can happen, can "un-happen" (i.e. reverse itself). This can be contrasted with macroscopic processes which are never perfectly reversible. This is one way that "the arrow of time" is seen. This problem remains unsolved and is recognized as one of the major fundamental problems in physics. We can't go backwards in time. So, we're limited to what experimental evidence we have when we talk about the "direction" of time.
You should also understand that the 2nd Law has no one single written form. It is expressed in different ways for different purposes. By this I mean that the word "spontaneous" need not be part of its expression.
See
https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Various_statements_of_the_law
https://en.wikipedia.org/wiki/Arrow_of_time#Arrows
(also Entropy_(arrow_of_time) and Entropy#Definitions_and_descriptions)
and maybe https://en.wikipedia.org/wiki/Equipartition_theorem
and of course Statistical_mechanics

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