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The expense was incurred in order to create a thermal gradient; which was diminished by the actions of the thief.

There should be a pretty straightforward relationship between expense and temperature of medium vs environment that would be amenable to simple mathematical manipulations suitable for a court demonstration.

Being that its a court, of course, the facts dont matter and it all hinges on whom each party is related to and which side's lawyers gave the judge the best hookers and likker at the country club.

Is that a kind of potential energy?
The judge's notion that the saline solution acquiring heat from the defendant's cellar equates to production/transportation of energy seems wrong to me.

Heat is not a desirable form of energy in this context, it's either a waste product created by the cooling system, or a naturally occurring element that is counteracted by the saline solution.

Maybe the judge isn't technically wrong, he just got it backwards. The energy here is expended to eliminate heat, while creating it would be the opposite endeavor.

Is this the reason why?

A good way to think about it would be "useful" energy vs waste energy. The energy used by a chiller to cool a cellar is useful energy. The heat (energy) that is removed from the cellar and rejected to the atmosphere is waste energy.

The defendant was stealing useful energy and returning waste energy.

The neighbor was stealing the coolness of the solution. Coolness was the desired/useful property, and it was taken for use in the neighbors cellar
Defendant was stealing negentropy (negative entropy, or order). Good luck explaining that to a judge!

Alternatively, it could be a claim of vandalism - the defendant didn’t steal anything, but rather damaged the saline by imparting energy on the molecules which disordered them.

I don't know why you were downvoted, I came to write the same idea.

The brewer paid for the energy required to clean the saline of unwanted energy, and the shop owner pollutes the saline by adding unwanted energy back into it, incurring an additional cost for the brewer as he must expend more energy to also remove the energy added by the shop owner.

Downvotes work in mysterious ways
We hit this (what seems to be a) paradoxon in a research project a few years ago, where we modelled production facilities that needed heat and cold at the same time (industrial bakery producing freezed goods, different pipes).

Since our goal was the optimization of energy flows, being able to use e.g. energy recovery of "waste heat", we could easily get paradoxical results, when counting with "hot" and "cold' energies.

The thing is, any medium can potentially carry energy (and in fact does), but if it is "usable" to you, depends on the difference to the environment you want to use it in/against.

400° hot oil? Net plus J in an oven, but net minus J for a chiller.

Yet, generating a certain amount of that hot oil took x Joule. Same goes for cold water or saline solution.

I think the plaintiff's argument was actually very fitting.

Mine is still not technical though.

That doesn’t seem to match. In this case, AFAICT, both wanted the cooling effect. No one wants the heat.

The saline solution was now being used to cool double the volume (2x the cellar space), so it seems pretty clear-cut to me — if saline cooling cost increases with volume being cooled, it should be trivial to say he’s now covering someone else’s costs. I don’t even see why we even need to bother digging into thermodynamics — looking at the cost structure of the cooling unit alone should tell us the answer. If there’s no relationship saline-usage-cost based on volume, then it still taken but no harm was done. If there is, then it’s trivial to calculate how much harm occurred

If one cellar was being heated, and the other cooled, then your paradox could be triggered (but it also seems to me the “paradox” is trivially resolved by double-entry accounting — the problem is simply in the name “waste”)

My understanding is that this is like borrowing water from your house and returning it into your septic system with “gratuitous” waste in it. It’s dumping entropy, or “stealing” a low entropy state on the plantiff. Not sure if this is the technical answer the article wanted though.
How can you complain? I borrowed plain old clean water and returned it with extra biomass, for free!
If you complained about a neighbor making your product dirty, this judge would say, "No, no, they're actually giving you free dirt!"
The energy he is stealing is the extra power he is causing to be used by the cooling unit, which is going to his benefit.

If I hook my house up to your house's electricity supply, it's the same thing. Even though you don't have less electricity than you had before, I have caused more to be used that you are paying for and I am taking and benefiting from.

I am in effect causing the electric company to sell you more power, which I am then taking for myself.

Seems to me that it would depend on the details. If the store just happens to be cooled because the pipes run closely by the store, then I'd say it's on the brewery to insulate the pipes. If the store rigged up something specifically to dump their heat into the pipes, then surely the legality would depend on how the property rights work for pipes running through the ground.
"Theft of thermal energy" or maybe "thermal state" may be a succinct way to put it. It applies to hot/cool that's being stolen and is agnostic to the energy required to create that temperature. I think that's the challenge here, finding a way to phrase it that would be acceptable to write in a judge's ruling
I strongly recommend the 'Futility Closet' podcast that accompanies the website. It is one of the most consistently interesting podcasts out there.
Basically every party that is contributing to the global warming can defend like this.
> The court of appeals ruled: “The saline solution acquires heat from the retailer’s cellar; therefore, energy belonging to the brewery is not being stolen. On the contrary, the brewery is receiving gratuitous energy from the retailer.”

Of course, there are cases where sending gratuitous energy to your neighbor clearly appears to be tortious. Like a high-powered laser weapon.

Is the retailer rerouting the coolant into his cellar, or just using the fact that his cellar is cold because of the proximity of the pipe?

If the latter, I'd say there is no theft- the brewer needs to insulate his pipe to prevent thermal losses.

“Your justice, how about I come to your house on a hot summer day and open all the windows and doors so the heat from the outside could give more energy to your air conditioner”
I have to agree with the judge here. The issue is not criminal theft here per the letter of the law. A lot of things that may seem like criminal theft to untrained eyes are not considered theft in the eyes of the law. For example, joyriding usually have to be added as a separate crime to criminal codes because they would not fall under the definition of theft in most jurisdictions.

That being said, the neighbour definitely has a civil case here and it should be easy to win that one.

Both judges are correct. The brewery needs a better lawyer. By the legal definition of “theft”, this ain’t it. They should sue for tortious interference (or whatever the equivalent under German law).
I talked to a non-techie friend and they had an interesting idea: that it was like going into a store and upsetting store displays. Creating a "mess" of disorganized matter (heated) that needed to be put back into order (cooled).
I'd also argue that this is more likely an interference than actual theft, to the effect that the owner has to invest more energy to achieve the same results he'd have without this interference, which ist the actual damage.
Thermal energy is heat. Not cold. Heat is being transferred from the retail cellar to the coolant.

The prosecution is right, they are paying to cool the retail cellar. But you can't produce cold, you can only remove heat.

The judge is MORE right, the argument that thermal energy is being stolen is not factual.

I don't see how this heat exchange could have been avoided. Why didn't the beer guy just get some more insulation?