I think the first law of thermodynamics could be restated as
\begin{equation}
\Delta U_S + \Delta U_{\Omega\setminus S} = 0
\end{equation}
i.e.
\begin{equation}
U_S+U_{\Omega\setminus S}=\text{constant}
\end{equation}
and this would clarify (to me) the relationship between the two concepts.

What you describe is a general law of conservation of energy; it assumes the rest of the universe (surroundings) can be ascribed energy and that the sum is conserved. The problem with this law is that we have no means of controlling the surroundings by definition, so it is (rather well-working) leap of faith.

The First law of thermodynamics is a little bit more restricted and more experimentally grounded. It concerns itself just with the system $S$, the surroundings are left unaccounted for.

It has more formulations which are more or less are equivalent. One of them is

*
Effect of heat supplied to the system on its state is equivalent to effect of certain equivalent amount of work supplied to it.$^{*}$ If both heat and work are measured in the same units (commonly Joules), a quantity characterizing the equilibrium state $X$, called internal energy, can be defined for allĀ $X$. After the system is supplied heat $\Delta Q$ and work $\Delta W$, internal energy changes by
*

$$
\Delta U = \Delta Q + \Delta W.
$$

(end of the law).

The change of $X$ and $U$ does not necessarily determine values of $\Delta Q$, $\Delta W$; they depend on the way the process is executed. The first law only says whatever the process (reversible, irreversible), change in $U$ is given by sum of heat and work supplied.

_{
$^*$ The work is to be done irreversibly in such a way as to mimic addition of heat, i.e. by stirring the fluid in the system. No amount of reversible work would make the system end up in the same state that addition of heat does (since addition of heat does not conserve system's entropy but reversible work does).}

At a given temperature, in your liquid water-air system, equal numbers of water molecules will enter the air from the liquid as return to the liquid from the air. The system will be in equilibrium and the air will be "saturated" with water vapor.

There are two ways that condensation will form on your ceiling. If the air is supersaturated with water then your "nucleation" sites will facilitate condensation. But conditions in this system are not those that would result in supersaturation. The second way for condensation to occur is for the ceiling to be colder than the air.

If condensation occurs on the ceiling, much of the latent heat of condensation will be transferred to the ceiling therefore warming it. To continue the condensation process, you will have to keep the ceiling cool requiring expenditures of energy from outside the system. Your system is closed but it is not isolated in thermodynamic speak.

Furthermore, as the condensing water loses heat to the ceiling, the system cools. This will result in a lowered equilibrium vapor pressure, that is, less water in the vapor state. To make matters worse, the lower temperature of your system will require an even greater lowering of the ceiling's temperature to maintain condensation.

As far a entropy, you must, in addition to events within your system, consider those happening outside to power the refrigeration process.

Hopefully you understand the turbine you may be running inside the system won't even come close to powering the refrigerator outside!

## Best Answer

The analogies between physics and finance are strong, so much so that the modern financial system is partly due to physicists, and mathematicians like Benoit Mandelbrot. But the applications usually come from random-walks and stochastic equations, which are related to quantum mechanics by analytic continuation in time. The ito-calculus of financial random-walks is nothing more than the Heisenberg algebra of quantum mechanics in imaginary time, where the momentum p is just $\partial_x$, without the factor of $-i$, and the commutation relation is $[x,p]=1$, without the $i$. This algebra of observables describes Brownian motion, and the short-distance structure of Brownian motion with drift, and market fluctuations, if parametrized with a time coordinate of volume traded, should ideally be a random walk or a Levy flight (walks with jumps). Further these Markovian processes need obey the Martingale property, meaning that the expected value of the asset in the future is the current value no matter how far into the future you look (compensating for the discount rate).

A random walk or Levy flight is completely stochastic and Markovian, so that each step is independent of the history. The definition of a Markovian martingale is a statement that you cannot make money by betting on stocks, just using past history as a guide. The prediction that this describes actual markets is based on efficient market hypothesis, the idea that any money that can be made has already been made, so that the remaining price fluctuations are purely Markovian. The only real evidence for the efficient market hypothesis that I see in the real world, and which is confirmed with physicist's standards of accuracy, is the hypothesis that asset prices are Markovian. If you open any newspaper and look at any price over time, you will most likely see a perfect Brownian motion.

The analog of inertia during transactions is a broker's fee, and when you can trade without a fee, there is no incentive to minimize volume, so you and a friend could swap a huge amount of a certain stock 500 times without loss, leading to fake-volume which will lead people to believe that there is a lot of trading interest in the stock. So ideal frictionless trading is a problem, and a transaction fee should incentivize against fake asset swaps of this sort, without unduly interfering with actual trades which both parties believe increase the value of their holding. I don't know the legal situation.

The recent collapse was partly due to the inability of agencies to estimate the risk of correlated loans failing simultaneously, and rating them as if they were independent. The independent risk model failed, and when property values fell below the threshhold required to make mortgage payments rational, nobody paid the mortgage, and the housing market collapsed.

There is no conservation law for wealth. The conservation law for money is violated by fractional reserve banking and central banks. The central bank is the source of money, it is amplified by fractional reserve lending at the banks, and there are several sinks, which consist of assets that drop in value, most spectacularly, a loan default. The economy just moves money from the sources to the sinks, and the rate at which it moves the money from player to player determines the income of the players.

The thermodynamic laws are not applicable here, since there is no good notion of stable equilibrium. The dynamic price equilibrium of markets is obviously a complex computing system, and not a dumb thermodynamic ensemble.