Of course, it is necessary -logically- to set up the following rules. But ... why was it found necessary to state it? If we are going to state logical rules shouldn't we include the rules of addition, subtraction, Boolean operators, all of set logic ? Where would it end?
Clearly, this statement is included because scientists think of these rules as "no longer physical". Rather, they have been elevated to the status of "proto-logical" entities.
There is a small discrepancy in the relationship between the 1st & 2nd laws (perhaps not on the part of professional scientists but in the teaching of the subject).
The problem is that the 1st law is not functionally related to the 2nd. The 1st law is a wholly deterministic-absolute on the observational level while the 2nd is completely statistical at that level. The second law only exists as a technicality. Its "proto-logical" status is dubious.
Here a gas escapes through the hole driving the vane whose rotation creates frictional heat loss into the surrounding space. It is statistically possible -in principle- for the gas molecules to return to the left side and thereby make themselves available for further vane turning. Thus, some would say that the 1st law is only statistical for it might be overturned by some wildly improbable Maxwellian sorting mechanism.
Of course, this is not so. Even if all the gas returns to the left side from the right side, no violation of the 1st law occurs. The returned gas would simply be cooler (on account of the heat escaping into the surrounding space by "vane" friction). Or, if that heat returns, the left side will be at the same temperature as the initial state.
Other rules of physics seem now to be thought of as having a statistical nature. In fact, none do this side of quantum mechanics (just the 2nd law of thermodynamics). And if one considers quantum mechanics to be the base of all existence -the current fad- one will inevitably be led back to absolutes. (See Determinism & Causality for an examination of this genuine dichotomy.)
There is some confusion about what constitutes an "ordered" state. To physicists white sand mixed evenly with black sand to produce gray sand is an ordered state but white sand separated from the black sand (in two separate piles) is a disordered state ( ! ) while entropy is considered in some quarters to be a state of maximum disorder ( ? )
If a meteor crashes to the Earth, this increases the entropy of the universe. But if all matter is spread out evenly (as in the early universe), this is considered a state of high order. And as matter falls down gradients of any sort, the entropy of the universe increases, i.e. it becomes more ...
Wait a minute ... I'm getting confused ...
There are two things to deal with here.
Note: Information is what we perceive as information. To the universe of inanimate matter, no matter how we arrange things the same amount of information is present (10011010001011 is the same as 11111110000000)The escape of a gas from a high pressure area to a low pressure area is an example of "sand mixing entropy". It is statistical in nature ... no gradient is traversed. When we release the gas its temperature drops but only if energy can be transmited to the walls of a container. It happens that this is always the case so that 'gas laws' concerning the relationship of pressure to temperature are "technically valid".
They are however not logically valid, i.e. if one could magically make the dimensions of a container smaller during the time that no gas molecule is in contact with any side of the container, the temperature of the gas would remain constant in the smaller container although the pressure would increase (more wall collisions per -now smaller- unit area per unit time at same temperature). Conversely, by symmetry, if the walls were increased in a reverse manner, the temperature would remain constant but the pressure would decrease.
This is a source of confusion among even professionals.
You cannot, in practice, contract the dimensions of a container in so short a time interval as exists between individual molecule-wall contacts. Therefore Boyle's observations seem to suggest a direct logical relationship. The true relationship is indirect.
Gas laws, as presently understood, imply that an energy transition is logically involved in the order-disorder relationship of matter confined to an equi-potential.Energy has nothing logically to do with order-disorder. The relationship is entirely technical. It takes energy to put the gas back into a container from which it has escaped but the activity is technical ... not directly logically necessary.
A gravity drop on the other hand ...has just such a logical relationship because the four forces are not statistical. The 1st law of thermodynamics is an absolute* (with quantum mechanical asterisks). So when an object drops down a gravitational gradient it loses energy when heat from its inelastic collision with the Earth is vented into space.
As the universe "clumps up", matter trades places with photons, i.e. photons diffuse into empty space increasing in number as the clumping process continues. Return all photons (& neutrinos) to stars-planets and all matter will heat up and unclump and restore the original high potential of the "maximum state of disorder" found at the origin of the universe.
But this is highly improbable ;o)
Do you get it now? If the improbable happened in this instance, matter heats up as a logically necessary concomittant. Probability is tied to energy gradients ... absolutely.
What then is entropy?Entropy is "clumping" ... falling down gradients. It is the increase in order (as perceived by us) ... NOT an increase in disorder as a confused scientific community would have us believe. The idea that it is disorder stems from the confusion over logical-technical details.