Thermoeconomics
The history of thermoeconomics is somewhat scattered and chaotic. For physicists, it appears to be a niche choice as the field turns towards industrial processes and the environment. Although the field doesn’t appear to have a concise or organised resource for its development, there are still several interesting publications that are worth investigating, although, for the sake of this section, we have opted to exact much of our focus on a particular article from 2009 by Annila and Salthe.
Looking at thermoeconomics’ popularity over time using google statistics (right), we see an obvious decrease in public popularity in the past 18 years. It is a shame the data only starts in 2004 as it looks very likely we have only an insight into the field’s decline in media.
In short, thermoeconomics is self-descriptive, the application of thermodynamics to economic studies. Ideas of increasing entropy, energy conservation, efficiency, free energy, etc. can all be applied to stock prices, business transactions/production, or optimal manufacturing efficiency, but the choice appears to be down to the author. In our case, we focus on a stock price model and can even opt to avoid entropy until the end.
Before getting into the minutia of any thermoeconomics, those areas of thermodynamics involved must be understood. This is the primary reason to the omission of variety in our choice of article – the background becomes far too complex and unintuitive in most publications. It appears the development of the core subject has stagnated, with more recent articles seemingly describing a specific application rather than theory. Regardless, if one is to read further into the field, having a more elementary starting point of comparison is of no inconvenience. The most important physics to brush up on beforehand is entropy if one wishes to follow our practical examples (although this main page can be understood without). [Note: from now on, links on this page take you to further reading and investigation, e.g. the entropy page above is a quick summary for those interested].
The easiest way to dissect Annila & Salthe’s equations/ideas are to start in reverse and work our way back, this avoids any detailed prior thermodynamics and abstracts can be drawn before the level of complexity is overwhelming. We can start by an initial thought experiment. Imagine two resources, each with an inherent worth but of limited supply, how is an exchange rate decided? It seems logical that a society bartering in these goods would eventually settle on an optimum ‘fair’ deal. A bigger discrepancy in prices would be accounted for more rapidly than a small one, like in the example figures below.
Take blue and orange to be those two resources, green initially being undervalued at $0 ($ is an arbitrary currency), and red at $100. The idea of currency is to be ignored still as there is no monetary exchange, but the ratio of the two would give the current bartering rates. Over time (fig.1, x-axis), red’s value falls while green’s increases, until eventually we find they are both worth $50. This is not, however, some incredible discovery as the code used to generate this figure already knows they should be of equal worth and models how our hypothetical society would realise it versus their previous evaluations.
This time (fig.2), the code is modified so that red should be more valuable as green but only by twice as much by ratio. Notice how they seem to change at the same rate to begin with, but level off and tend to their final values much quicker. That rate of change of commodities is referred to as their velocity which depends on several factors including the current value of all the commodities including itself.
We notice that the velocity of a commodity appears to be larger the farther it lies from its final value but is not an indicator of what this final value takes (as these two examples start extremely similarly).
Introducing a third and then up to 7 commodities (fig.3, 4), returning to equal target worth, affords us no surprises. In both cases, the initial velocity of green is much larger versus blue (not cyan) which follows from the intuition we have built. When two commodities start at the same value however, they follow an identical path, like cyan and red in fig.4 where red is obscured. This seems unlikely in a real-world scenario.
Finally, we can add as many commodities as we like and randomise both their initial and target values. Starting with 7 again (fig.5), we see some slightly more complex behaviour occur in pink as it starts by increasing and then falls a little while later. This is a much more interesting shape than the figures we have seen so far which initially appeared to be simple log curves. The assumption we tried to apply of the velocity being an indicator in final value does not hold true anymore as this pink curve has a gradient of zero in two places – perhaps there is an idea there to do with the second derivative (alike to the commodity’s acceleration)..
Then bumping up to 30 commodities (fig.6), any complex behaviour like before is seemingly hidden amongst the magnitudes of the more sweeping changes. Now is a decent time to note that the and axes vary in number, but this is due to repeated changes in the code. The time and values are simply measured in arbitrary units which would follow from the input data given to the model.
How could this be applied to a real-world economy in any useful fashion? We already covered that the system effectively requires the final values anyway, so how would one profit from using this model if it cannot provide any useful extrapolation forward in time?
Notes & Opinion
The topic of thermoeconomics was introduced in the sixties and its popularity in physics, as seen, has tapered off in recent years – during the advent of AI and machine learning. If the complex behaviour observed in fig.5 (above) was absent, one could be confident that, given a fraction of the data in the beginning, a machine could (learn to) nicely fit curves to make a prediction. However, even without accounting for the infinite complexity of the stock market, this is not the case, and a great deal of effort would have to be applied to reap any benefits. Why bother when an AI may as well learn directly from historical data rather than a concoction of theory and application? It feels that this may be the main reason why this field appears to be becoming overlooked in research: drawing analogies to classical physics is not as necessary as when the idea was first presented. However, its modern use appears to be developing in environmental science and farming. The papers are very technical so, to be frank, we are not confident in claiming we know why.
Summary
More knowledgeable readers, recapped on the ideas of entropy, may wish to modify the python to track the total entropy change of the universe in this process. Of course, we would expect this to be positive, but we cannot assume the model’s truthfulness. Real-life stock charts have much more noise and variation than the smooth curves shown here, how would random noise affect the total entropy change? Is there a maximum feasible entropy change? And if so, could one exploit that limit for profit?
Without improving the model significantly, and a willingness to enter a segment of the entire stock market’s historical data, there is no way to tell how accurate the analogy of energy to currency is. It feels intuitive and certainly produces a satisfying result, but that is in no means a good indicator of performance without a comparison.
Test your knowledge! And take a look at a speedy derivation of thermoeconomic velocity below.
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External Link to Article
The idea of this thermoeconomics section is to read the main page first and then repeat, the second time including the extra information from the four links. Any animations from this (TsarKy) youtube channel were made by us using the ManimCE python library.
Reading on
If this page has piqued one’s interest, be sure to search for “thermoeconomics” as if it were plural. Otherwise, many convoluted models may present themselves. We suggest taking a look at:
The Evolution of Physics in Finance
Completed by: Jake Wilkes, James Penston, Sam Jones and James Lundie.
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