ThermoeconomicResearch

Economic value is not an abstraction. It is energy expended, entropy produced, work performed — and it obeys the same laws as everything else that does.

Commissioned & applied

Reports

The applied write-ups — narrower than the theory, worked through to a number, and priced because they take the framework somewhere specific. $20 each, delivered as PDF. The full research corpus further down this page is open access and always will be.

AEM Report №1
Thermoeconomics

The Thermoeconomic Operator: Energy, Entropy & Value

A formal treatment of the thermoeconomic cost function — how energy expenditure and entropy production ground monetary value in physical law.

AEM Report №2
Mining Economics

SHA-256 Mining: Bitcoin vs. Quai Profitability

A comparative analysis of mining economics across Bitcoin and Quai Network, with real-world hardware data and energy cost modeling.

AEM Report №3
Physics of Computation

Computational Irreducibility & Causal Invariance in PoW

How Wolfram Physics concepts — computational irreducibility and causal invariance — provide the theoretical substrate for proof-of-work consensus.

What a purchase gets you

Derivations, data, and the assumptions written out

Including the ones we are least sure about. Where a report depends on a model, the model is specified well enough to be re-run and disagreed with. Bulk and institutional licensing available on request.

thermoeconomics.info · the framework

Where physics
meets economics.

A computational framework connecting energy, entropy, and proof of work to the foundations of economic value. Not a metaphor borrowed from thermodynamics — a formal isomorphism, derived and defended in full.

The central claim is narrow enough to be wrong: a monetary unit that cannot be produced without expending energy inherits a floor from thermodynamics, and that floor is computable rather than asserted. Everything downstream is an attempt to hold that claim to account.

The framework is assembled from four independent lineages that were never meant to meet. Each arrived at the same boundary from a different direction. Thermoeconomics is the argument that the boundary is the same one.

Lineage 01 · Entropy

Information and heat are one quantity

Shannon showed information carries a mathematical structure identical to thermodynamic entropy. Jaynes turned that identity into a universal inference engine: given limited information, maximize entropy. Wolfram asks whether the universe is itself a computation, and irreversibility its signature.

Lineage 02 · Distributed computing

Time in a network is logical, not physical

Lamport proved that without a global clock, logical ordering is the only coherent notion of time in a network. FLP proved guaranteed consensus in an asynchronous system is impossible — which is precisely what makes probabilistic proof of work the theoretically correct answer rather than a compromise.

Lineage 03 · Energy

Computation has an irreducible physical cost

Landauer established that erasing a bit dissipates real heat — at minimum kBT ln 2. Bennett showed even reversible computation cannot fully escape the floor. Information is not an abstraction sitting above physics. It is physics.

Lineage 04 · Proof of work

Where the theory became a protocol

Hashcash made computational cost a currency of attention; Nakamoto turned it into trustless accounting. Proof of Entropy Minima then reframes the mechanism as a provable statement about entropy rather than a race for hashes — which is what finally makes work comparable across architectures.

Selected results

Three claims the framework is willing to be judged on.

Pmin = VC(S(ER))

The monetary floor

The market capitalizes the thermodynamic sacrifice of proof of work into the value of the monetary unit, creating a liquid claim on future energy. A floor with a derivation rather than a promise.

ΔS = 2−n

Information as rank

Threshold methods are lossy compression — they discard surplus entropy reduction. Ranking outputs by absolute value extracts the maximum information available, and reaches the physical limit of finality.

E ≥ kBT ln 2

Energy as numeraire

Beneath every bit erased there is an irreducible cost, verified experimentally. Gold rewards stockpiling; energy rewards production. Denominating in the one input every industry requires aligns capital with expansion.

Visit thermoeconomics.info ↗

The ontology

The tech tree

The claim sits at the top. Everything below it is what it had to stand on — seven layers, each load-bearing for the next. Nothing in the field is asserted without the layer beneath it in place.

6 · Field
Computational Thermoeconomics
5 · Application
Token & Controller DesignMining Economics & DifficultyFat Tails, Options & PortfoliosAI Infrastructure & Neuro-Symbolic Agents
4 · Synthesis
Energy = Cross-EntropyProof of Entropy MinimaThermoeconomic GeodesicsHash Possibility SpaceHolographic Sharding
3 · Systems
Distributed ConsensusCryptography & Hash FunctionsWolfram PhysicsActive Inference & Bayesian Mechanics
2 · Inference
MaxEnt & Bayesian InferenceInformation GeometryFluctuation TheoremsThermodynamics of Computation
1 · Foundations
Probability & StatisticsShannon Information TheoryThermodynamics & Statistical MechanicsTheory of Computation
0 · Ground
Complex Systems & Emergence

Open the tech tree ↗

The corpus

Published work

Nine papers and theses, open access, every one with its derivation shown. Listed newest first.

FrameworkJune 2026
4 pages

The Thermoeconomics of Computation

Steph Macurdy · Wolfram Research

All computational work sits on a continuous spectrum bounded by pure entropy production at one end and pure free-energy extraction at the other. Treating the kilowatt as both the constraint and the medium of exchange, operators face a strict opportunity cost between routing power to cryptographic consensus or to AI inference — and the global equilibrium closes into a thermodynamic loop where energy secures the ledger and intelligence optimizes the next kilowatt.

Kilowatt Opportunity CostExpected Free EnergyLogistic FunctionLandauer Limit
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PaperDec 2025
11 pages

A Thermoeconomic Operator

Steph Macurdy · Wolfram Research

Every proof-of-work protocol anchors to the same physical phenomenon — repeated hash-based Bernoulli trials whose outcomes are IID. This paper connects that process to the Maximum Entropy Principle and the Generalized Boltzmann Distribution, the only distribution where Gibbs-Shannon entropy equals thermodynamic entropy. The blockchain is read not as a ledger but as an operator: a machine converting physical work into informational order.

Maximum EntropyBoltzmann DistributionPoEMFormal IsomorphismQi Emission
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ReportNov 2025
24 pages

Qi / Quai — Controller Report

Andrius Kulikauskas PhD, Math4Wisdom · commissioned by Steph Macurdy

Can active inference or thermodynamics say anything rigorous about the relationship between Qi and Quai? A commissioned investigation of the dual-currency system through energy, entropy, and free energy — mapping the control mechanism, analyzing miner incentives, and building a bridge to the Free Energy Principle. Qi maps to belief in the system; Quai to belief in belief in it.

Active InferenceDual CurrencyFree Energy PrincipleGame TheoryGresham's Law
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FrameworkJune 2025
3 pages

From Ontology to Computation

Steph Macurdy · American Energy Money

A compact roadmap from physical reality to computational work. Ontology, mathematics, epistemology, and computation are argued to form a sequential dependency chain rather than parallel disciplines — bounded above by thermodynamic law and grounded in the insight that information is physical.

OntologyLandauer's PrincipleShannon EntropyComputation
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Thesis
56 pages

Economic Observer Theory

Steph Macurdy, Wolfram Blockchain Labs · Wolfram Model sections by Justice Evans-Hunter

The long-form treatment, running from the computational observer through the Principle of Computational Equivalence to the origins of symbolic value. If observers are computationally bounded and equivalent to what they observe, then price, temperature, and pressure are the same kind of object — reductions an end-directed observer extracts from an irreducible world in order to spend less work.

Observer TheoryComputational EquivalenceSecond LawSymbolic ValueRuliology
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Thesis
44 pages

Quantifying Work, Eliminating Time, and Minimizing Entropy

Steph Macurdy, Wolfram Blockchain Labs · Wolfram Model sections by Justice Evans-Hunter

Consensus has always been a clock problem. Bitcoin bound time to state in the timechain, and every scaling effort since has been an attempt to loosen that coupling. The argument here is to remove the clock entirely — ordering events by causal invariance rather than timestamps — paired with a dual-token architecture that tokenizes cost of production directly in energy.

Causal InvarianceEntropy MinimizationMultiway HypergraphsDual TokenEnergy-Backed Money
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Essay
29 pages

The Wolfram Model

Steph Macurdy · Wolfram Model sections by Justice Evans-Hunter

A guided walk from A New Kind of Science to the Ruliad — cellular automata, computational equivalence, irreducibility, hypergraph rewriting — showing how space, time, relativity, and quantum branching emerge as artifacts of how a finite observer samples. Closes with an even-handed account of the program's reception, including its shortage of falsifiable predictions.

Cellular AutomataThe RuliadIrreducibilityObserver Theory
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Thesis
14 pages

Engineering with Irreducibility

Steph Macurdy · Wolfram Blockchain Labs

An integrative framework for emergence tracing a path from Wolfram's computation to Deacon's teleodynamics to Nakamoto's proof of work. Computational irreducibility is recast not only as a limit on what observers can know, but as a tool engineers can deliberately impose — a boundary condition for cultivating emergent behavior.

EmergenceTeleodynamicsVia NegativaSymbolic Value
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HandbookJan 2025
30 pages

Core Ingredients of Blockchains: UTXO Handbook

Ignacio Calderon de la Barca & Steph Macurdy · UTXO Alliance

An open-source visual reference to the Unspent Transaction Output model and the design variations built on it. Nine member chains diagrammed side by side — Bitcoin, DigiByte, Cardano, Ergo, Nervos CKB, Quai, Topl, Alephium, Hathor. Design variety comes from how the ingredients are combined, not from what they are.

UTXO ModeleUTXOChain DesignInteroperability
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Applied elsewhere

Where the theory turns into something you can trade or meter.