The molecules of liquids and gasses both attract and repel each other because of spatially distributed electrical charges of their molecules. They are also in a continuous so called Brownian motion where all molecules hit others exchanging speed and energy, the faster ones loosing energy to the slower.
Both within liquids and gases speed distribution a normal or Gaussian because they hit each others every time at a different angles and positions respect to the position of the electric charges presented at collision time which means in both phases more molecules move close to average speeds and fewer close to smaller and higher speeds.
However there are big differences in speed between the two phases, liquid and gaseous. In a closed container that holds liquid at bottom and gas on top fewer molecules in gaseous phase move much faster in order to create the same pressure and temperature as those much more numerous in the liquid phase below.
They do it because only at higher speeds they can brake the electrical bonds between them.
We also have to consider the simple fact that a molecule with a spatially distributed electric charge and weight would have a rotation energy.
In liquid phase molecules rotate less mostly oscillating because they have to stay bonded with each other. For this reason their distribution of speeds or entropy is smaller than for gases. The model is also complicated because they all move within a gravitation field which acts to completely separate the liquid and gaseous phase.
Some of the total energy of molecules moving withing a gas or liquid or the so called thermal agitation is stored in the rotation momentum, not only straight linear or curve line motion momentum (because of reciprocal attraction or repelling of the electric charges their trajectories between two hits might not be a straight line but parables or more complicated ones).
So after all, the so called difference in entropy between gases and liquids could be nothing more than difference of rotation speed component of molecules within the two phases.
Turning a gas into a liquid involves bonding of the molecules and stopping of their rotation movement or reducing it to wave oscillation within a matrix.
Also. When compressing the gas molecules with a linear reciprocating motion compressor on average we do not add rotation but only linear motion and when cooling them after compression like in an AC we extract mostly rotation because the solid molecules on the side of the pipe vibrate mostly around a rotating point but do not move freely.
https://www.google.com/search?q=liquid+dipole+dipole+interaction
https://www.jstor.org/stable/984598?seq=1#page_scan_tab_contents
But what happens to the thermal agitation within the liquid if all molecules are attached to others in more than one point? Will they vibrate as a piece of jello? Are they constantly breaking just to get immediately attached to others? Probably both depending on the temperature and of course at the surface near the interface there will be more breakages and reattachment then at depth.
From this google search however we can see there are many theories about this extraordinarily common, complex and overlooked phenomenon of which none seem to completely follow the intuitive dynamic molecular approach i'm trying to describe here.
https://www.google.com/search?q=liquid+gas+interface&source=lnms&tbm=isch
If we completely remove air from a container filled partially with a liquid then close it will instantly boil until it will fill the vacuum with gas that achieves the necessary pressure for the two phases to coexist but due to gravity the liquid phase will separate at the bottom and there will be also a membrane like separating surface between the two also due to electrical attraction between molecules in liquid form at the surface.
https://www.google.com/search?q=water+bubble+in+space&source=lnms&tbm=isch
However there are other theories that say the membrane is more of a wave like structure with an ever changing shape.
"This series of experiments led to consideration of some profound questions about the nature of the gas/liquid interface, particularly when distances are measured in nanometers. At this scale, liquids don’t have a sharp edge; rather the transition to a gas occurs slowly and is often “wavy.” Tiny “capillary” waves create a dynamic surface on liquids that look a lot like a rough sea to the molecules on both sides of the interface. And, the shorter the length scale under scrutiny, the rougher things get. To a molecule, a “placid” liquid surface can look like a snapshot of water boiling!"
https://jila.colorado.edu/research/chemical-physics/chemistry-gasliquid-border
We may always have spatially distributed changes in the normal distribution of molecular speeds and densities next to the surface of a stable liquid-gas closed system with changes in temperature which may be measurable or subject of computer simulations and eventually used as a power source.
"It is shown that the presence of the temperature gradient at the interface due to evaporation leads to reduction of the surface tension. The results of MD simulations are in agreement with the results of thermodynamic approach."
http://aip.scitation.org/doi/abs/10.1063/1.478779
"previous simulation studies have mostly examined the bulk thermodynamics of water evaporation, treating water as a continuum, and neglecting effects tied to individual molecules." "Each time a liquid water molecule enters the vapor phase, a coordinated dance of several molecules is involved, according to simulations."
This is one step closer to prove that molecules that evaporate have a minimal and narrow speed range and as soon as they are in gas phase they start absorbing energy from the other molecules just to get at "normal speeds" and this is where one part of the heat absorption through evaporation happens.
But for that molecule to survive above surface it needs a first hit from the molecules of the walls of the reservoir or from another molecule coming from behind that eventually gets back in the liquid loosing its energy. Otherwise it will be hit from one above and return to water with more or less energy than when it escaped while that molecule hitting from above will loose some energy by hitting a slower one and a domino effect will start and a temperature gradient will be created.
By removing the fast molecules on top with a compressor or even with a fan more lower energy and lower entropy molecules from liquid will raise, creating a bigger temperature gradient.
https://physics.aps.org/articles/v8/118
Let's now talk about heat pumps. If for the practicality of this demonstration we use a liquid with boiling point @ environmental temperatures and pressures and instead of a reservoir we partially fill a radiator made of a winding pipe and start extracting gas from it with a compressor, there will be more room for molecules in the gas phase, the pressure will decrease and the liquid will release more molecules but only at speeds close to thermal vibration of the liquid which are much slower thus colder than environment that would start to the fill volume and heat up or catch molecular speed from the molecules of the pipe of the radiator due to temperature difference with environment while cooling the radiator and the gas towards the end of the pipe next to the compressor will have again normal speed distribution and environmental temperature though at lower pressure.
The compressor will have a side effect and that is heating up the gas at temperatures higher than environment because of the movement of the piston that accelerates the moving molecules. So we can add a second radiator right after the compressor with a valve at the end that holds pressure called relief valve that would cool the gas with the relief valve connected back to the first radiator in a closed circuit.
At some point the compressed gas inside the second radiator will start to cool and turn into a liquid but at a higher pressure.
Molecules in the second radiator at some point through cooling though at higher pressure will start to pair or form chains or clumps with much lower average speeds than gas because as liquid they have to stay within the speed limit of breaking the electrical bonds of molecules at that pressure for existing as liquid.
Then the relief valve that holds the higher pressure at the end of second radiator ensuring cooling of the freon at higher pressure inside will let liquid freon go back into the first radiator at a lower pressure when it starts turning into gas again or restart the cycle from the beginning. And this is the description of design and working of the current heat pumps and ACs through molecular dynamics interpretation. Of course there are formulas and all pressures and parameters and capacities of different components that have to stay within certain limits for the whole system to work efficiently but mainly this is how it works.
***
I think the main phenomenon is: fast and slow molecules during compression all collapse into electrical bondage at the same speed or energy regardless of their initial speed while loosing their extra energy to the environment in the second radiator due to higher temperature and pressure created by the compressor in the same time being released from bondage during decompression in the second radiator at constant speeds or spead of electrical bonds breakage instead of random and higher speeds thus decreasing entropy for the system.
Also in the second radiator the system dumps energy by slowing speed for every molecule individually, no matter what its initial speed until their speed is right for pairing or bonding it with another molecule to become liquid and removing it from the gas and this can be done only at higher pressure and temperature than the environment with the help of the compressor also decreasing entropy for each molecule individually.
This happens again through molecular selection. Only those with right speed, no higher will turn into liquid at the surface.
If faster molecules end up inside the liquid phase, their heat or energy will be distributed in the rest of the liquid and lost at the contact with the pipe and cooling it while the others will continue hitting each others in the walls of the pipe of the radiator loosing speed and heat or energy to the colder molecules of the metal pipe which in turn looses is to the environment until new ones are selected.
In the end all molecules with random speeds will end up in the liquid phase with more constant speed and position and at evaporation emerging molecules are selected like in Maxwell's thought experiment with the extra heat lost in the environment in the second radiator.
