Thermodynamics & Blockchain, part 2. Proof of Stake

John Small
14 min readApr 29, 2019

In the first article in this series I pointed out that Schrodinger’s observation that living things ‘drink negative entropy’ from the environment to maintain internal order is relevant to blockchains. Living things use a system similar to Proof of Work to maintain records and transcribe records. See Thermodynamics of Blockchain and Thermodynamics of Life . I ended with a question, it’s obvious that Proof of Work consensus is a thermodynamic process, there’s lots of heat, but what role does thermodynamics play in of Proof of Stake (PoS) and Delegated Proof of Stake (DPoS) consensus based cryptocurrencies? Not only that but systems that implement Byzantine Fault Tolerance accept records as unchangeable once they’ve been decided on by a committee. Which implies they must be generating more entropy than PoW systems which have only probabilistic finality. Which is weird. Why is that?

It’s subtle…

Continuing the theme that ultimately the second law of thermodynamics has to be the basis of creating immutable records, and also that living things have had lots of practice over billions of years doing this, we’ll try to understand what’s going on in PoS and DPoS.

Switching out of the clear physics of Bitcoin mining, and the similar biophysics of RNA translation gets us into slippery concepts of ‘belief’, ‘stake’, ‘community’, ‘governance’ and the like. It’s hard to see the connections with thermodynamics which must be there somewhere. But out of the mists outlines of forms start to appear and we can begin to see where cryptocurrencies are heading, how they fit into future society, and usefully where investment should be directed.

PoS & Thermodynamics in communities

Let’s jump in to get better feel for how thermodynamics works in PoS consensus. First of all you have to see that even the archetypal PoW cryptocurrency, Bitcoin, contains elements of being a Proof of Stake currency, it’s not obvious because it’s not made explicit.

Consider a simple thought experiment. Supposing a large state decided to amass enough hash power to mount a 90% attack on Bitcoin. E.g. Russia (not impossible), could accumulate mining rigs and then run a parallel chain for a bit with more accumulated work than the main chain, then reveal it to clients and other miners. According to the formal rules of Bitcoin, other nodes would have to switch to the chain with more work. But would they? It’s more likely that people would get together and decide to keep the old chain going because the Russian BTC (Ruscoin or RusTC) had been compromised. A 51% attack can’t reverse people’s memories. The total entropy of the old Bitcoin chain plus the memories of people in the Bitcoin community considered as a complete system would be greater than the the Ruscoin system even though Ruscoin might have 90% of the hash power of the Bitcoin chain. That’s because the total entropy in Bitcoin is more than the total entropy created by mining, it’s also in the community that shares the records.

In fact Satoshi alluded to this in his original paper on Bitcoin

The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post

Satoshi Nakamoto 2008 see

The key is in the words “widely publishing the hash”. Spreading out the information gets it thoroughly mixed in to the environment so that the entropy is increased and by the Second Law of Thermodynamics, it’s hard to reverse. Like stirring milk into coffee, you can’t unstir it.

If the Bitcoin community decides that there’s an error in the chain then the community can reverse it. This already happened with Bitcoin in 2010. A bug in early Bitcoin code allowed someone to create a very large number of Bitcoins. See That time someone hacked 92 billion BTC into existence . The fix as described in the article was simple ;-

The community simply hit ‘undo’, jumping back to the point in the blockchain before the hack occurred and starting anew from there; all of the transactions made after the bug was exploited — but before the fix was implemented — were effectively cancelled.

The community had a stake in Bitcoin (like PoS) and wanted it to succeed, so the Bitcoin community leaders at the time and others had sufficient authority (like Proof of Authority), to overrule the Proof of Work algorithm. This also happened with Verge another PoW coin. see Verge Is Forced to Fork After Suffering a 51% Attack. The Verge community forked Verge to reverse the effects of the 51% attack because they had stake in Verge being successful. Similarly a 51% attack on Ethereum Classic was stopped by community intervention. I.e stakeholders did something to overrule the double spends that happened.

Because there are more independent components in the community around a blockchain, i.e. more degrees of freedom, there is greater total entropy in the community of people spread out all over the world than that generated by mining. Distributing the information over thousands of memories in people’s brains creates more entropy than mining so it’s harder to reverse.

Therefore we can identify at least two components to the entropy that makes Bitcoin records hard to reverse. There’s (1) the entropy created by mining, and (2) the entropy created by distributing the information recorded to thousands of people. In fact so much entropy is created by widely distributing the information recorded in the blockchain that we can abandon (1) and just rely on (2) to make records irrevocable. Which is in essence how Proof of Stake systems work.

The evolution from Proof of Work to Proof of Stake is similar to the evolution of money from physical metal coins to pieces of paper, to records in computer memory. It used to be the case that ‘money’ was represented by pieces of hard to obtain metals with insignia on them authorised by a central authority. But it was tedious to carry bits of metal around so people put them in safe places called ‘banks’ and received promises on paper which says in effect ‘I promise to pay the bearer on demand the sum of X amount of physical metal’ (In fact up until 1968 it was possible to redeem some dollar bills for physical silver see Silver certificate (United States) )

Hard to obtain metals are like hard to obtain computing power. Conservation of mass and energy can be used to create unfakeable records, so people trust them as records. But they’re inconvenient to carry around, so a piece of paper stating that the metal exists is good enough. Once enough people have come to a collective agreement to accept records of rights and obligations represented by indicators of physical metal or expenditure of energy, then you can remove the actual metal or spending of energy and just rely on the collective agreement in a community to accept the records as if the real physical stuff was there or as if the real energy spending computations had happened. In PoS we accept the records as if real energy spending computation had taken place.

There’s an analogy (only an analogy!), with magnetising iron. In an unmagnetised iron block all the atoms have random magnetic orientations. You then expose the iron to an external magnetic field. That lines up all the orientations so that the iron block becomes magnetised itself, and then sustains its own magnetisation. (This feature is important and will be explored in a future article where I’ll discuss statistical field theory and its application to ‘social field theory’)

Only after a community of people have accepted that (nearly) irrevocable records of rights and obligations can be created without a central government authority by using cryptography and vast computing power will they accept that similar (nearly) irrevocable records can be created without a central government authority by using cryptography, but without the vast computing power. PoS systems would never have been accepted without people first getting used to the idea of cryptocurrencies by using PoW systems.

Because PoS and DPoS are not rooted in the physical constraints of PoW systems they are just as much fiat money as present national currencies, they both rely on the shared beliefs of a community to sustain their value and determine how they are issued.

This is where we have to get into fuzzy concepts like ‘shared beliefs of a community’ which are far away from nice clearly defined concepts like heat, pressure and ATP molecules. That’s because we’ve had to think about the entropy contained in a community of people not just the physical computers running a blockchain. But ultimately there are ubiquitous principles that apply at the scale of collections of atoms and also at the scale of societies.

A full review of PoS and DPoS and Byzantine Fault Tolerance is outside the scope of this article, which is to look at the thermodynamics of these methods. But you can get up to speed by reading A Proof of Stake overview, Tendermint Explained — Bringing BFT-based PoS to the Public Blockchain Domain, DPOS Consensus Algorithm — The Missing White Paper and Ethereum — Proof of Stake FAQ and Blockchain Consensus Encyclopedia — More than 72 Blockchain Consensus described

In summary there are two main flavours of PoS based consensus (I’m including DPoS in PoS). Chain based or Byzantine Fault Tolerance (BFT) based. Although most PoS systems are a mix of PoS and BFT. In essence they’re all different ways to convince a community of users that the records written into the distributed database are valid and are not going to be changed. They rely on creating entropy by distributing information widely so that records are hard to reverse.

In a pure Proof of Stake system, and anyone could take part and block production would be randomly allocated according to cyberwealth. Just as block production in PoW is randomly allocated according to hash rate. In a pure chain based PoS, we retain the notion of a chain of blocks, selecting the longest chain to be the definitive chain. In terms of the Consistency, Availability, Partition Tolerance (CAP) theorem , it’s choosing availability over consistency in the case of a network split. When the nodes in the network reconnect they’ll be able to work out which chain is longest, and decide that one is the definitive chain. Which means some records can be deleted. The longest chain has the most entropy and is hardest to reverse. But just like PoW this is only probabilistic finality.

In contrast BFT systems choose consistency over availability in case of a network split. But they create definite finality as soon as more than 2/3rds of a defined set of validators commit to a block. This is very odd. It seems that a small set of people, which therefore has a lower number of degrees of freedom, can reach a state which is impossible to reverse faster than a larger set which has more degrees of freedom and hence more entropy. Why?

Simple. It isn’t irreversible. But the community pretends it is.

Once a community accepts BFT consensus as be as valid as if lots of computing power had been dedicated to mining to find a block, then it’s a short step to getting the community to accept that BFT consensus is valid as if the block had been found with the maximum difficulty setting in PoW. Which would require an almost infinite amount of computing power to reverse, and hence a network reorganisation can’t happen. But the reality is that if the community decided to reverse the records it wouldn’t take much computing power to do it. However the amount of fuzzy ‘social computing’, politics, argument, and changing people’s minds to allow a record to be reversed is very large.

However the shift from PoW to PoS systems because it places emphasis on the community has focused attention on issues of governance and control. In PoW you can cheat by mounting a 51% of the hash power. In PoS/DPoS systems you have to use political manoeuvering to take over the system.

Although that also happens in Bitcoin because it is secretly a PoS system which depends on the ‘stake’ community members put in. Which is why different communities now run different versions of Bitcoin.

People with votes in a PoS/DPoS system might not directly generate bad blocks, but they might very well interfere with the governance of the blockchain project in ways which benefit themselves at the expense of the entire community supporting the project. This appears to be happening in the case of Lisk, see Lisk — the mafia blockchain .

Living things use PoW do they also use PoS?

In the first article in this series (Thermodynamics of Blockchain and Thermodynamics of Life) I pointed out that spending energy to reliably create records is a key evolutionary step that life took nearly 4 billion years ago. PoW works in ribosome transcription from RNA to proteins and in DNA replication. Living things drink ‘negative entropy’ or ‘order’ from their environment to maintain genetic material in a very low entropy state while exporting high entropy, which makes the reactions hard to reverse. The entire system of DNA, RNA and all the cellular machinery is a very low entropy system and it needs to access sources of ‘order’ to keep it that way. That costs energy.

Since PoS is theoretically more energy efficient we should expect that living things would have exploited some sort of PoS system to maintain their low entropy systems. But they haven’t because things like ‘community belief’ don’t translate easily into molecular biology. Or have they? Maybe things are more subtle.

‘Stake’ relies on community. It’s the community that gives value to records and therefore creates value in the ‘stake’. Also ‘stake’ represents commitment to a community. We’re expecting people who put up a ‘stake’ will not do something that damages the community and hence the economic value of that ‘stake’. It’s very wobbly reasoning and relies on an unproven chain of trust which is why people are rightly cautious about switching from PoW to PoS. But living systems do have something similar to a chain of trust.

Stake in the community

In the world of bacteria there’s a problem with parasites. There are lots of viruses that try to inject their genetic material into the bacteria to get the bacteria to replicate it. These viruses are called bacteriophages (because they eat bacteria). In response bacteria have evolved many ways to prevent this, and bacteriophages have in turn evolved many ways to get around the preventative measures. There has been a constant arms race between phages and bacteria since living things first evolved (see Bacteria vs. Bacteriophages: Parallel Evolution of Immune Arsenals). Fighting off phages is very energy intensive. Phages are one example of the fact that as Schrodinger pointed out, low entropy is a valuable resource, therefore other things will be constantly trying to get at it. When a phage infects a bacteria, it uses the low entropy of the bacteria to create copies of itself, and in doing so destroys the bacteria. From a thermodynamic point of view the complexity of the bacteria, which is order and therefore low entropy, is replaced by lots of less ordered things, i.e. higher entropy. Parasites are an expression of the Second Law of Thermodynamics which is that entropy always increases. Parasites occur at all levels of complexity in the organisation of life. From bacteria, to animals, to societies and political systems.

One of the most significant evolutionary steps to counter phages has been to hide away the machinery of replication inside a walled off nucleus so that phages have to cross a substantial barrier to get to it. This is the eukaryotic cell.

A eukaryotic cell is vastly more complicated (is more organised and has lower entropy) than a simple bacterium. Life got started a few hundred million years after Earth was formed, but the eukaryotic cell took a couple of billion years more to evolve. It’s a very complex system of teamwork between living things that started out as independent entities. In other words a eukaryotic cell is a tiny community (see From prokaryotes to eukaryotes). Each component of that tiny community has a ‘stake’ in the survival of the community. The genetic material and the molecular machines to replicate it are stored away in a centralised nucleus. Which makes it hard for phages to infect. Though of course viruses have evolved to get into the nucleus. But having a nucleus and having lots of community members which try to stop viruses getting to the nucleus does mean less energy is spent keeping the genetic material intact. There is something like a chain of trust so that if a message gets in to the eukaryotic nucleus it is assumed to have ‘stake’, because it’s been passed in by all the other components of the cell which do have a stake in its survival. This lowers the amount of energy the nucleus has to expend defending the genetic records against viruses. So I suppose in this sense life has evolved a Proof of Stake system. But it’s not nearly as obvious as the ribosome Proof of Work system. But this is centralisation!! Horror!!!

Centralisation, efficiency and EOS

Centralisation makes information processing more efficient. It’s a lower entropy system than being decentralised. But because it has lower entropy and things want access to sources of low entropy for their own purposes, there is a danger of the central core being taken over by a predator or parasite. Which is the reason why people don’t like centralisation. Most of the time a centralised system works well for a community because division of labour allows a large amount of information to be processed, but if the centralised system is ever taken over then there is no back up a community can switch to.

Living things have had billions of years dealing with the problem of how to preserve records when malicious agents are trying to disrupt that process for their own selfish purposes. Cryptocurrency projects are replicating many of the methods already worked out by living things. Centralisation done right is one of the things living systems have worked out.

For example compare this diagram of the EOS system

Image by Jack Tanner. 2019

With this diagram of a eukaryotic cell.


In both cases there’s a central, heavily protected region that looks after making the records. In EOS it’s the block producers. They’re linked on fast networks with each other, they have military grade security protection and no direct contact with the outside world. Surrounding that are nodes that handle the communication between the block producers and the outside world. In the eukaryotic cell the machinery of DNA replication, record keeping, querying the DNA, and transcribing it to RNA, takes place inside the nucleus which is protected by the nuclear membrane. It has no direct contact with the outside world and has the biological equivalent of military grade security. Various molecular messengers carry information from outside the cell to the nucleus to tell it which bit of DNA need to be ‘queried’, i.e. transcribed into RNA, and got working.

In a sense the evolution in structure from Bitcoin and Ethereum into EOS is analogous to the evolution in structure from prokaryotic cells, without a nucleus or much structure, to the eukaryotic cell which has a nucleus and a very complex structure. (see From prokaryotes to eukaryotes)

So if cryptocurrencies are replicating the evolutionary paths life has taken, then the next step will be ‘multicellular’ organisms. E.g. lots of interconnected EOS like chains.

But we also have to consider the evolving ecology that these systems create and live in. Cryptocurrencies are a way for communities to come together and exchange value between members without the restrictions of national borders. There’s a very interesting phenomena that occurs in all systems composed of individual units which affect each other. It’s called phase transitions, and we can see the early stages of that in the crypto world. Understanding how that works provides a valuable insight into where crypto is heading.

That’s the next article in this series.



John Small

Developer with maths background. Keen on crypto currencies and understanding their place in social and political evolution. See