Blog of Veikko M.O.T. Nyfors, Hybrid Quantum ICT consultant

Quantum Mechanics demystified, a try

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Everything is made of molecules, which are made of atoms, which are made of subatomic particles.

Entropy, it is describing the order in which molecules and atoms are in the non-visible diminutive world. The smaller the entropy, the more ordered molecules are. The bigger the entropy, the more mixed up molecules are.


Entropy and heat are closely related.
In thermodynamics, below formula defines the change in entropy to be the heat energy put to the system divided by the overall temperature of the system.

$\Delta S = \frac{\Delta Q}{T} \hspace{1em}$ (T in Kelvins)

Think of you having a Saunabath. A 9 kw stove has heated for an hour, and temperature in the sauna itself is now about 90⁰C. You throw water on the stove, and the feeling is awesome.
Once you finish, you turn off the stove and leave the door open. Temperature in shower room was 24⁰C originally, as it was in the sauna to start with as well.
Later in the evening you come back to shower room. The temperature has raised a bit, say to 28⁰C. When you close the door to sauna, you see the temperature there is also 28⁰C now. Temperature has become even on both rooms.
Entropy in practice, that is.
Per the formula above, we can say entropy in the sauna and shower room complex has increased by

$\frac{9000\frac{J}{s}*3600s}{297K} = 109090 \frac{J}{K}$

Second law of thermodynamics states entropy always increases or stays the same in a closed system. It never decreases. As a consequence of that heat always flows from hotter objects to colder ones. Never the other way round.

$\Delta S \geqslant 0$

Meaning universe is pursuing towards homogeneous temperature. Matching the dynamic energy in the very beginning, before big bang.
One can reverse this locally though, but you need to apply external energy. You can e.g. freeze an ice cube.

Heat in itself is vibration of molecules. And of atoms and particles those are made from. The more jiggling, the warmer it gets.
We feel the warmth, as our sensors (in fingerprints and elsewhere) start to jiggle more rapidly. We see the temperature rise in thermometer, as molecules in hotter air makes molecules in thermometer go faster. Which makes indicator to rise.
Or vise versa. In cold our fingers start to getting chilled and thermometer drops down as their molecules give some of their jiggling away.

Heat being movement, this makes sense. Think of having a molecule moving faster than another, i.e. having bigger momentum. When they hit each other, the faster gives some of it’s energy and momentum to the slower one. Faster will slow down and slower will speed up. Never vice versa: slower one would never get even slower and the faster one would never get even faster. Sounds so obvious. Don’t know how to prove it though. Yet.
That is, if we do not take it as a proof, that when you throw an ice cube to Mediterranean Sea, it melts instead of getting a bit colder.


Thermodynamical entropy is involved with molecules vibrating in different paces striving to equilibrium throughout the system in question.

Heat, or the trembling molecules, increase homogeneity even if no heat would get transferred. Thus general randomness in the world increases. World is striving towards homogeneity, also otherwise than just with temperature.

Imagine you pour darkblue Curacao liquer to a class of sprite and white rum. All of them at the same temperature. You add the ice afterwards :-)
The whole class becomes light blue in time, even if you do not stir it yourself. Which you might have a hard time not to do :-).

Similarly, all over, things get mixed to each other, if they are left alone. Trembling molecules are bumping to each other and mixing up little by little.
Babylon was a mighty town three or so thousands of years ago, but is all ruined now, as it was left alone with no upkeeping.
Bodies will turn to dirt after death if not empalmed or something.


In thermodynamic context, specific closed system are irreversible in entropy sense. I.e. $\Delta S \geqslant 0$
This doesn’t apply to entropy in randomness way. In there, it is a question of probabilities.

Having two molecules bumping to each other, that’s a reversible process. That’s provable by Newtonian mechanics.
Having four molecules bump, the same applies.
Imagine you playing 8 ball billiard. You start the game, none goes to pocket. How much you would like to return to the starting triangle. No problem. If you were able to apply a reverse force simultaneously to each ball, which they got in the last impact, they would neatly return to the triangle. That is if environment remains the same in every aspect.
Well, that’s not so easy anymore, is it? There is 15 + 1 balls involved, you see.
When it comes to the light blue curacao drink, with ~ $10^{25}$ molecules, it becomes practically impossible to have molecules return back to the original separation. But in theory, if each and every molecule at one moment would be effected by a reverse force to the previous impact force, they would do so. That is, again, only if the environment was identical in all moments going backwards as it was when going forward.

Fuzzy and blurred nature of human perception

Human perception is not on molecular scale, nor scales down from that. We do not see how molecules are arranged on that minuscular scope.
Instead, what we perceive is macroscopic view of that diminutive world. Passed to our eyes by photons, emitted by electrons in material around us when they drop down on their excited energy levels on atoms forming the molecules.
This view is the fuzzy and blurred image of how molecules and atoms are laid out between themselves.

Having a look on the light blue curacao drink again. With ice and all.
It isn’t likely we would at some point start to see dark blue stripes or something alike in the glass. No matter how long we let it be.
With a smaller set of molecules, though, I would imagine they could probably arrange themselves in a way that all the blue ones are together on one spot and all the rest elsewhere.
Would be nice to arrange an experiment with say 10000 molecules to see how long it takes them to rearrange into order.
Or to suffle a brand new deck of cards so many times, that they will be back in original order by suites and numbers. Actually, to have the deck suffled into any preselected specific order is as hard as having them back in factory order.

In the end it is a question of probabilities. Odds having whole class full of molecules to rearrange so that blue curacao molecules would be separated from the clear ones, is just so incredibly small, that we feel it is impossible.
Odds having the molecules in any other specific order is as improbable as well. However, such a big portion of these specific orders only show up the same to us as being light blue.
If we had a look on molecular level, we would see that at any instant the molecules would not be evenly mixed up. Rather they would be mixed up in some other specific order. So close to evenly scrambled that it appears to us as such. Number of specific orders showing up as light blue is so incredibly vast, that odds to have one of those at the moment we look at the glass is close to 1. We will (most) always see a light blue drink.

Bolzmann’s entropy formula

$S=k \cdot \ln{(W)}$

To try to understand what this means, one has to remember what entropy is: thermodynamic entropy is the measure of molecular disorder at a specific macrostate of the system, i.e. in which pressure, temperature and volume the system is.
Bolzmann’s entropy formula tells this measure is logarithmically dependent on the number of arrangements of molecules, or microstates, bringing out the observed macrostate of the system, timed with Bolzmann’s constant $k=1.380649x10^{-23}$.
In the end, it gives kind of a probability of the system being in a specific macrostate.

In our saunabath illustration entropy was small to start with, as number of microstates producing 90⁰C in sauna and 24⁰C in the shower is very small. Final status 28⁰C all over has far more possible microstates, thus entropy is way higher then.

Trying to make this easier to comprehend, let’s think it is only eight molecules in the whole of sauna compartment. In original situation four hot molecules were in sauna itself and four chiller ones were in shower. In final situation all eight molecules have same temperature, meaning each and every one can be in either of the rooms.

Initial situation has only one possible microstate. $S=1.380649x10^{-23}*ln(1)=0$
Whereas final situation has 9 possible microstates: \(S=1.380649x10^{-23}*ln(9)\) which gives entropy of \(3.0*10^{-23}\).
Not much sense in this sample either.

Nor even any practical sense in case with all molecules involved, other than entropy has increased over time.
Where would we use these absolute figures for entropy anyway. If someone can give a hint, I would be grateful.