# The Thermodynamics of Mixing

Mixing is a well known concept in physical chemistry. If you mix 2 ideal gases, what is the driving force that causes gases to mix, and what causes the mixing to become uniform? Ideal gases don’t react so there is no energy transfer due to chemical change in the constituents. So what is the driving force? The answer is entropy or something called the Gibbs free energy of mixing, in a formula dG = dH – TdS. dG is change in free energy, dH is change in enthalpy, T is temp and dS is change in entropy. In an ideal gas, dH=0 and T is constant, so the formula simplifies to dG = -TdS If dG is negative the mixing occurs spontaneously and it will mix until ALL of the molecules are thoroughly mixed. Once thoroughly mixed the potential to mix (dS) reaches zero, that is when entropy reaches it’s maximum and no further mixing will occur. There are plenty of youtube videos and wiki like sites to more fully describe this process.

The reason I bring this up is this is what drives the virus? Humans are like one ideal gas. Virus is like another ideal gas. The planet is the reaction vessel. The virus mixes by embedding itself into humanity in a manner that is a similar (but not the same) set to 2 ideal gases mixing. As the infection progresses the virus attains a bigger mole fraction further increasing the drive to entropy this would be like H in the above equation becoming a negative value and since H can be a function of time dH/dt as long as it stays negative it can grow exponentially. Thinking about this relationship we have to conclude there is not going to be any Hammer and Dance solution to the virus. The mixing will occur until the Gibbs free energy of mixing goes from negative to zero. If dG goes negative again mixing will again occur. That is precisely what we are seeing. When locked down dG effectively went to zero (Rt < 1). The lock down was cancelled Rt > 0 and means dG once again goes negative and mixing progresses. A vaccine since it interrupts the virus’s ability to mix effectively forces dG=<0 interrupting mixing.

So now you have a mathematical model upon which to base your judgments. If different states have different Rt’s it merely means they are at different places on the mixing surface. It does not mean they are handling things in a superior way, since the driving force is entropy. NY once had a Rt in the 0.8 range, today 1.05. This means dG has gone from zero back to negative and infection will continue until entropy is satisfied.

In anesthesia we measured drug effect in half lives. The curve to equilibrium was asymptotic and it took about 5 half lives to reach 90% of equilibrium (when entropy is satisfied). if we just divide the population into 1/5 ths and use that number as a half life, it means 1.4B people per half life. Herd immunity is about 80% of the population therefore 5.6B people is herd immunity. We are at about 12M worldwide infections.

A vaccine is not a cure. A vaccine is merely a substitute or competing infection. The virus or it’s competing substitute will continue until entropy is satisfied to a level of 80% herd immunity. Never in the history of humanity has a vaccine been created in a couple months so banking on that is like banking on the lotto. As old people die off, young people will take over. Much knowledge and critical productivity is contained in old people that is not contained in young people so a society of young people will be left to reinvent the wheel and reinventing the wheel kills productivity. Dead productivity = a dead market, so be careful when you glibly chop off the geezers. In addition if it’s geezers who are dying what about people who survive? There is significant morbidity associated with this disease. If you infarct 50% of your LV it stays infarcted and you become a cardiac cripple. Knock off 70% of your kidney function by micro infarcts and you’re on dialysis 3 days a week. There is a condition called pump brain where protracted bypass causes cognitive decline post bypass. It’s a soft sign kind of decline but something like this brain fog seems to be happening. Children seem to be showing neurological changes on brain scans. In Hong Kong I read a report that 25% of post infection survivers had long term lung problems and SOB. Do a quick thumbnail on the increased medical cost and lost productivity of this morbidity. Seems to me dying is the least of your problems if you get sick.

If nothing else Covid dumps a load of unmeasured volatility into the system likely long term. If you get the volatility wrong you are more likely to get the truth wrong. That’ll mean you’re long when you should have been short. The next time your Governor is up quacking about Covid and what a swell job he/she is doing you can think back to the Gibbs free energy of mixing and see if they really have a clue. My presentation is about similar sets not about perfect correlation. Certainly there are particular aspects of infection that deviate the model from ideal gases, but the model points you in the right direction. If you have N, S, E, W, to choose from and the model suggests N, go N.

I ran across this video. If you think this recovers like the flu think again.

## 3 Replies to “The Thermodynamics of Mixing”

1. LearningToFish says:

Dear Gasem,

Right now I am learning financial concepts such as Sharpe ratio , Efficient Fronter , Equity Beta , Alpha , sequence of returns risk etc

Can you recommend any blog , podcast , book , video etc that does meticulous DIY investment analysis (with graphs and charts) and also could teach us how to perform similar DIY investment analysis ?

Also , a blog by someone who is regarded somewhat as a gadfly , contrarian or miscreant that dares to question conventional financial wisdom?

Thanks a million for all you are doing.

Stay safe in Florida.

1. mdonfire says:

Hi LTF I don’t know of any website that does a credible analysis of “HOW TO” in a step-wise fashion. Investing is not simple and investing is not political. Neither is investing like it was 10 years ago. The stock market no longer acts as a price discovery mechanism for an equity, but is a flow discovery mechanism which looks at momentum and leverage. Most of stock trading is done either by algorithms or passive funds. In this time of COVID 25% of the volume is from retail accounts run by novice investors who don’t have the first clue what they are doing. Hertz is 100% bankrupt but these retail accounts bid it up to \$6. This isn’t investing this is a game of hot potato. Some will get burned some will get rich but either way it’s gambling, but we pretend it’s investing. The trading algorithms are agnostic on direction. They will go short just as easily as they go long and they will go short like a pile driver if the momentum indicates that. Algorithms analyze data and rate of change second order data something the average human doesn’t understand. Humans think in linear space, AI thinks in exponential space. Humans think in terms of surface area, AI thinks in 3 or 4 dimensions or fractally. So while the human sees a little piece of ice sticking out of the ocean, the AI sees under the surface and based on probability determines the iceberg below and the risk of sailing close to the little tip of ice sticking from the surface.

Sometimes like today there is a complete disconnect. We live in a real world, but we invest in a virtual world, a video game kind of world. In the real world I may own a hand gun. In the virtual I may own a Bradley fighting machine. Only problem is my fighting machine isn’t real, it’s a simulation, it’s a narrative, it’s a picture on a monitor. If I invest my real money based on the narrative and I am unaware of things like the real demographics, leverage, risk, FED manipulation, politics, civil unrest, the narrative will happily eat my money. The narrative is designed to eat my money.

To understand how to invest don’t look at return. Return is a prediction and a presumption. What you have to understand is risk. When you buy a risk asset, what you actually buy is risk. Risk is the chance to make money and it’s also the chance to loose money. Risk changes in an exponential fashion Read my article Eve of Destruction and look at the picture. As long as you’re risk is in the linear part of the column, your path is extremely predictable. This linear part of the trip is what the narrative is based on. Above the linear part the risk turns rotational around an eye. Here risk looks like a hurricane with the little eye staring up at you. Kinetic energy is defined by KE= 1/2 MV^2 note this is a exponential function. As V increases energy increases by an exponential proportion. Risk is an exponential variable, so learning how to manage risk and not be controlled by the narrative is the key.

I like Real Vision as a source. They are a subscription service so it will cost some money but they have a huge library. I like Hedgeye also a sub service but they have some youtube videos as well. Hedgeye does teach you how to trade or think about trading. I like George Gammon youtube videos. He teaches a lot about the underlying economy. For example last week 50.1M unemployment applications were made or continued. The government by the end of the year will have pumped 5T or so into the economy. The QQQ is up 17% YTD. 50M unemployed is far far from normal. 5T is far far from normal. In this scenario what is the similar set? The QQQ up 17% is far far from normal given the other 2 in the set. The narrative is “a V recovery”. You have a choice buy some risk or don’t buy some risk. If you buy some risk is the risk asymmetric? What is the chance of a double? What is the chance of loosing half? What is the chance the narrative is wrong? What is the chance Hertz stays in business? How can the QQQ be up 17%, but the banks are down 37%?

I’m not buying any QQQ. Someday I will but not today. If you want to understand the risk of investing it’s going to cost some money. If you want to understand someones narrative you can pretty much get that for free or maybe the cost of a book or something. Look at the free youtube stuff by real vision hedgeye and gammon and go from there. The idea investing is simple is also a narrative that sells books.

2. LearningToFish says:

This is one super impressive thought provoking reply.

For a macroeconomic view , I have been going to
https://podcasts.apple.com
and look for any podcast that interviews these economists.
Lacy Hunt , Kiril Sokoloff , David Rosenberg , Grant Williams

They have a dim view of the current high stock market prices.

Thanks a million for all you are doing.