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Thermal Macroeconomics: An axiomatic theory of aggregate economic phenomena

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Pith's one-line read The paper claims exchange economies admit an economic entropy such that every possible transition between aggregate states increases or preserves it, and one function yields temperature, market prices, and the direction of money flow.

desk verdict A serious, internally clean axiomatic translation of thermodynamics to exchange economies, but the load-bearing extensivity assumption is self-admittedly unrealistic and the abstract oversells the no-microfoundations claim. read the letter →

arxiv 2412.00886 v3 pith:5JFJJAW4 submitted 2024-12-01 econ.GN physics.soc-phq-fin.EC

N.J.Chater , R.S.MacKay This is my paper · ORCID
classification econ.GNphysics.soc-phq-fin.EC MSC 91B0291B5080A05
keywords economicentropythermalmacroeconomicssecondlawofeconomicsexchangeeconomytemperaturemarketpricesmoneycapacityaxiomaticthermodynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that exchange economies — systems in which fixed total amounts of goods and money are merely redistributed by trade — carry a thermodynamic structure: there exists an economic entropy $S$, unique up to rescaling and adding constants, and a transition between aggregate states is possible exactly when it does not decrease total entropy. If this 'second law of thermal macroeconomics' is right, it provides a purely macroeconomic foundation for market prices, the value of money, inflation, and the Le Chatelier–Samuelson response relations, without any assumptions about the rationality of individual agents. It also supports new predictions: money flows between economies in financial contact in the direction set by an economic temperature $T = 1/(\partial S/\partial M)$, each good acquires a market price, and a trader can extract money from temperature differences with the efficiency of a Carnot cycle. The derivation applies the Lieb–Yngvason entropy representation theorem, which turns a comparison relation plus scaling and convexity axioms into a real-valued additive entropy, and the paper illustrates the result on a toy exchange economy of Cobb–Douglas agents (pairwise exchanges biased by a power-law utility), whose entropy is $S = N\log((G/N)^\alpha (M/N)^\eta)$.

What carries the argument

The central object is the economic entropy $S$, and the machinery that produces it is the Lieb–Yngvason entropy representation theorem, which builds a real-valued, additive, extensive entropy out of a comparison relation once the relation is a pre-order compatible with scaling and convexity. The economic reading supplies those ingredients: the trader-mediated accessibility relation $\preceq$ (a state $Y$ is reachable from $X$ if a trader with unlimited goods and money can effect the change with arbitrarily small net change to the trader's external system), the financial-equilibrium relation $\equiv$, and the extensivity axioms A4 and A5, which say an economy can be scaled by any positive factor $\lambda$ and sliced into $\lambda:(1-\lambda)$ parts. The derived quantities do the explanatory work: coolness $\beta = \partial S/\partial M$, its reciprocal the economic temperature $T$, the value $\nu = \partial S/\partial G$ of a good, and the market price $\mu = \nu/\beta$ at which reversible exchange between good and money is possible. For pure money the entropy takes the exact form $S = K\log M + F(G)$, which makes temperature proportional to the money stock and gives a constant money capacity $C = K$.

What would settle it

The paper itself proposes a direct test: measure the entropy change between two aggregate states along two different quasistatic paths, using $\Delta S = \int \beta\,dM + \nu\,dG$ with $\beta$ and $\nu$ inferred from measured temperature and prices, and check that the result is path-independent; any path dependence means entropy is not well-defined. A second concrete test is to place two simulated exchange economies in financial contact and check the claimed direction of money flow: money must move from the economy with larger $T = 1/(\partial S/\partial M)$ to the other and stop when the marginal aggregate utilities of money are equal, so a single observed flow against the temperature gradient in an economy satisfying the axioms would refute the stated second law.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the set of transitions an economy, or a compound of economies, can undergo is not arbitrary: under axioms A0–A15 the accessibility pre-order is represented by a real-valued entropy $S$, unique up to orientation-preserving affine transformations, with $X \preceq Y$ if and only if $S(X) \leq S(Y)$ for comparable states of equal weight. From this the paper derives the Second law of thermal macroeconomics — putting two or more exchange economies into contact in any way cannot decrease total entropy — and, from the single function $S$, the economic temperature $T = 1/\beta$ with $\beta = \partial S/\partial M$ (the marginal aggregate utility of money), so that under financial contact money flows from the hotter to the cooler economy; the market price $\mu = \nu/\beta$ of each good, with $\nu = \partial S/\partial G$, at which no net trade occurs; the money capacity $C = \partial M/\partial T$, whose positivity makes inflation a well-defined aggregate notion; and, for pure money, the exact form $S = K\log M + F(G)$. The paper verifies the axioms on the Cobb–Douglas toy economy, derives quantitative conditions for mutually beneficial trade and a Carnot cycle for extracting money from temperature differences, and obtains macro-level analogues of the Slutsky, Hotelling, and Le Chatelier–Samuelson relations.

Load-bearing premise

The load-bearing premise is extensivity — axioms A4 and A5, that an economy can be scaled up or down by any positive factor and cut into arbitrarily small pieces without changing which transitions are possible; the paper itself states that this 'is strong, and unlikely to hold in general in many aspects of real economies' because of economies of scale and discrete agents, and without it the entropy representation, the second law, temperature, and prices all collapse.

Editorial extensions

If this is right

  • In financial contact between two simple economies, money flows from the hotter to the cooler economy and stops only when their economic temperatures are equal (Section 12).
  • Every good has a market price $\mu = (\partial S/\partial G)/(\partial S/\partial M)$ at which a trader's offer causes no net exchange, a macroscopic existence-of-prices result that does not rely on individual rationality (Section 14).
  • A trader running an economic Carnot cycle between economies at temperatures $T_H > T_C$ converts money leaving the hot economy into profit at efficiency $1 - T_C/T_H$, and the reverse cycle moves money against a temperature gradient at a bounded coefficient of performance (Section 18).
  • Any removal of trade barriers between exchange economies yields non-negative gains of trade for the union, independent of the order of trades; but free-for-all trade need not raise every economy's entropy, and only mutually beneficial trades increase all individual entropies (Section 19).
  • Concavity of entropy delivers macro-level versions of the Le Chatelier–Samuelson principle, the negative-definite Slutsky matrix, and Maxwell/Hotelling-type symmetry relations among price and quantity responses (Section 20).

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the entropy function can be estimated from real data through path-independent $\Delta S$, the framework would supply a basket-free, macro-level measure of inflation and of the value of money that could be compared against price-index measures; the paper leaves this estimation as an agenda rather than doing it.
  • The toy model makes temperature proportional to $M/N$ and inversely proportional to the agents' bias strength, which suggests a quantitative micro-to-macro test the paper does not run: in simulated exchange economies, measured temperature should fall as trading noise is reduced, approaching zero in the fully rational limit.
  • The Carnot-cycle efficiency bound can be read as an upper limit on profit from frictionless arbitrage between economies at different temperatures; checking whether real capital flows respect $M_H/M_C \leq T_H/T_C$ would probe the theory's reach beyond exchange economies.
  • If extensivity fails only mildly in real economies, the theory should hold approximately, and the path-dependence of measured $\Delta S$ — the same observable that tests the theory — would double as a diagnostic for where the macroeconomic second law breaks down.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper develops an axiomatic 'thermal macroeconomics' for exchange economies. It adapts the Lieb-Yngvason axiomatic formulation of thermodynamics, introducing an accessibility relation and a financial equilibrium relation, and deduces the existence of an additive economic entropy S, unique up to orientation-preserving affine transformations, such that a transition between states of exchange economies is possible exactly when total entropy does not decrease. From this entropy the paper derives an economic temperature T = 1/(∂S/∂M), money capacity, goods' values and market prices, and then uses these concepts to analyze trade, tariffs, the Carnot-cycle analogue, the Slutsky matrix, and the Le Chatelier-Samuelson principle. A Cobb-Douglas microeconomic toy model is used to verify the axioms and to compute S explicitly. The theory is explicitly conditional on a set of axioms A0-A15, and the authors acknowledge that the most demanding axioms, especially scalability (A4/A5), are unlikely to hold for real economies.

Significance. If the axioms hold, the paper delivers a remarkably strong representation theorem: a single aggregate entropy governs all transitions and prices, without direct microfoundational assumptions about individual rationality. The import of the Lieb-Yngvason theorems is rigorous, and the Cobb-Douglas toy model is internally consistent and its axioms are checked in Appendix A. The paper also makes concrete falsifiable predictions, such as the direction of money flow from high-temperature to low-temperature economies, the economic Carnot-cycle efficiency, and sign restrictions on cross-derivatives; the companion simulation work cited as [LMC] is a further strength. This is a genuine and careful contribution to the long-standing programme of thermodynamic analogies in economics, going beyond earlier proposals by proving existence of entropy rather than assuming it. Its significance, however, is conditional: the domain of validity is restricted to extensive exchange economies satisfying A0-A15, a class that is not shown to include any realistic economy, and the paper itself concedes that the central scaling axioms are likely to fail in real economies.

major comments (3)
  1. [Section 8 and Section 10] The extensivity axioms A4 and A5 are load-bearing for the existence of an additive entropy. Theorems 1 and 2 of Lieb-Yngvason, which are the source of the entropy function S and hence of the Second Law (Section 10), the temperature (Section 12), the money capacity (Section 13), and the market-price formula (Section 14), require scaling by arbitrary positive real λ and slicing in arbitrary λ:(1−λ) ratios. The paper itself states in Section 8 that scalability is 'strong, and unlikely to hold in general in many aspects of real economies' and notes that discrete agents break exact scaling; the only micro-verification offered is the Cobb-Douglas toy economy of Section 11, which is scale-invariant by construction. This is not a peripheral caveat: if A4/A5 fail, the representation theorem does not apply and none of the derived aggregate relations is guaranteed. The manuscript should either prove an entropy representation under weaker assumptions (for example, Giles-style integer scaling, or a quantitative bound on the violation), or reframe the central claims as theorems about extensive exchange economies only, with the non-extensive case explicitly outside the theory's scope.
  2. [Section 4 and Section 6] Axiom A0 (unique statistical equilibrium) and Axiom A13 (transitivity of financial equilibrium) are strong structural assumptions that the paper does not prove for any non-toy economy. The paper itself gives examples where A0 fails, such as herding and multiple equilibria (Section 4), and notes that A13 'might not hold exactly for real economies' (Section 6). Because A0 defines the state space and A13 is needed for the equivalence-relation structure used in Theorem 2, the paper should either characterize a class of exchange dynamics that provably satisfies these axioms, or state explicitly and prominently that the theory applies only to economies for which these axioms are empirically satisfied.
  3. [Section 9 and Sections 12-14] Axioms A9 (unique support plane) and A10 (connected boundary of forward sector) are needed for differentiability of S, which is in turn required for the temperature, money capacity, goods' values, and market prices. The paper gives no economic argument for these assumptions beyond calling them technical. If a forward sector has a kink, the entropy is not differentiable and the market-price formula µ=ν/β is not defined. The authors should either prove A9/A10 for a natural class of micro-founded exchange economies, or discuss what economic phenomenon would produce non-smoothness and whether the derivative-based results survive in subdifferential form.
minor comments (5)
  1. [Section 1] The text 'highly accuratecausalmodel' is missing a space and should read 'highly accurate causal model'.
  2. [Section 8] The footnote suggesting that scaling by positive integers might suffice is directly relevant to the validity of Theorems 1 and 2 and should be promoted to the main text, since the paper's own viability depends on this issue.
  3. [Section 16] The sentence 'to establish whether they might could be developed' contains a grammatical error ('might could') and should be rewritten.
  4. [Section 20.2] The symbol ð in equation (16) is not included in the list of notation; it should be defined there or in the surrounding text.
  5. [Abstract] The phrase 'without relying on implausibly strong rationality assumptions over individual microeconomic agents' appears twice in the abstract; one occurrence should be removed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: entropy is constructed from accessibility axioms via Lieb-Yngvason rather than fitted to target predictions; temperature and price are derived consequences, and the toy model is micro-founded.

full rationale

The central derivation is a direct application of the Lieb-Yngvason representation theorem: under axioms A0-A15, an economic entropy S is constructed to represent the accessibility preorder ≾, and the Second Law is the explicit 'if' direction of Theorem 2 applied to the operation of putting economies in contact. This is a theorem consequence, not a fitted parameter renamed as a prediction; the paper itself notes that LY treat the second law as the existence of entropy with the property of Theorem 2. Temperature T=1/(∂S/∂M), money capacity, goods values ν=∂S/∂G, and market prices μ=ν/β are all derivatives of the same S, and their stated behavioral properties (money flows from high T to low T, reversible exchange at μ) follow from the axioms on financial equilibrium and concavity, not from tuning S to match macroeconomic facts. The Cobb-Douglas toy economy's entropy S=N log((G/N)^α(M/N)^η) is computed from an explicit stochastic agent dynamics and its stationary Dirichlet distribution, not imposed to reproduce macro price or Slutsky results; the axioms are checked for that model, not assumed by fitting the entropy. The self-citations present ([M25a], [M25b], [LMC]) concern ergodicity of the illustrative model, a fluctuation identity, and simulations; they are not the load-bearing route to the general entropy, temperature, or price theorems, and they do not smuggle in the target results. The strength and plausibility of A4-A5 is a domain-limitation concern: if those axioms fail, the Lieb-Yngvason representation theorem does not apply, but that is a correctness/scope risk rather than a circular reduction of a prediction to its inputs.

Assumptions & free parameters 3 free parameters · 6 assumptions · 4 invented entities

The central contribution is conditional on a set of strong domain axioms (A0, A4, A5, A13, A14, A15). The toy model contributes two hand-chosen micro-parameters (alpha, eta) and the theory inherits unit-like calibration constants from the Lieb-Yngvason framework. The invented quantities (entropy, temperature, money capacity, pure money) are mathematical constructs with in-principle measurement procedures but no direct real-economy validation in this paper.

free parameters (3)
  • CD goods exponent alpha = alpha > 0 (e.g., 1 in Figures 2-4)
    Parameter of the toy Cobb-Douglas micro-model. It sets the value of goods and the market price mu = (alpha/eta) M/G. Chosen by hand, not fitted to macroeconomic data.
  • CD money exponent eta = eta > 0 (e.g., 5/2 in Figure 2)
    Parameter of the toy micro-model. It sets temperature T = M/(N eta) and money capacity C = eta N. Chosen by hand, not fitted to data.
  • Entropy calibration constants a_k = positive constants (Theorem 2)
    Lieb-Yngvason's Theorem 2 requires choosing multiplicative constants to calibrate the entropy scales of different simple systems so that total entropy represents accessibility in product systems. These are degree-of-freedom constants, analogous to choosing units, not fitted to reproduce the claimed predictions.
assumptions (6)
  • domain assumption A0: any closed exchange economy settles to a unique statistical equilibrium state.
    Section 4. The whole state-space formalism requires a unique stationary distribution for given amounts of goods and money in each connected component. The authors acknowledge that herding or multiple equilibria would violate this.
  • domain assumption A4: extensivity: scaling an economy by any positive real number preserves the accessibility relation.
    Section 8. Required for the Lieb-Yngvason entropy representation. The authors state that this is 'strong, and unlikely to hold in general in many aspects of real economies'.
  • domain assumption A5: any system can be subdivided into parts in arbitrary ratio lambda:(1-lambda) with (lambda X, (1-lambda) X) reversibly accessible from X.
    Section 8. Needed to define multiple scaled copies and additivity of entropy. Cutting connections in a finite system changes fluctuations of order 1/sqrt(N), so exact reversibility is an idealization.
  • domain assumption A13: financial equilibrium is transitive.
    Section 6. If A is in financial equilibrium with B and B with C, then A with C. The paper notes this excludes cyclic money flows, an approximation that might not hold exactly in real economies.
  • ad hoc to paper A14: for each state X there are states X_0, X_1 with X_0 equiv X_1 and X_0 ≺ X ≺ X_1.
    Section 7. This non-degeneracy condition ensures temperature-order and accessibility cross; the authors provide a plausibility argument using cloned economies and a reversible trader, not a proof. It is specifically introduced to make the entropy construction work.
  • domain assumption A15: for any states of two simple systems, one can add a non-negative amount of money to one to achieve financial equilibrium.
    Section 6. Needed to compare temperatures and derive the temperature formula. It presumes continuity and that money is a suitable numeraire.
invented entities (4)
  • economic entropy S independent evidence
    purpose: An aggregate, cardinal utility-like quantity that governs all possible transitions of an exchange economy through the second law.
    The paper proposes measuring S via economic calorimetry (Section 16) and cites simulation tests in [LMC], giving a falsifiable handle in principle, though no real-economy data are presented.
  • economic temperature T independent evidence
    purpose: Governs the direction of money flow between economies in financial contact; T = 1/(dS/dM).
    Falsifiable through the predicted direction of money flow (money flows from high to low T) and through the proposed financial thermometer (Section 16).
  • money capacity C independent evidence
    purpose: Quantifies how much money must be added to raise temperature; inversely related to the inflationary impact of money creation.
    Can in principle be measured from the T-M relation; positivity is derived from concavity of S. It appears in testable relations such as Var M = C T^2.
  • pure money
    purpose: A theoretical limiting case of money with no intrinsic value, leading to S = K log M + F(G) and constant money capacity; proposed as an approximation to modern fiat currencies.
    It is an idealized construct, but it yields concrete predictions such as prices proportional to the money supply, which could be tested in controlled experiments or simulations.

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Pith. "Pith review of Thermal Macroeconomics: An axiomatic theory of aggregate economic phenomena." pith.science (2026). https://pith.science/paper/5JFJJAW4

@misc{pith2026241200886,
  author       = {Pith},
  title        = {Pith review of: Thermal Macroeconomics: An axiomatic theory of aggregate economic phenomena},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5JFJJAW4}},
  note         = {Machine review of arXiv:2412.00886}
}
read the original abstract

An axiomatic approach to macroeconomics based on the mathematical structure of thermodynamics is presented. It deduces relations between aggregate properties of an economy, concerning quantities and flows of goods and money, prices and the value of money, without any recourse to microeconomic foundations about the preferences and actions of individual economic agents. The approach has three important payoffs. 1) it provides a new and solid foundation for aspects of standard macroeconomic theory such as the existence of market prices, the value of money, the meaning of inflation, the symmetry and negative-definiteness of the macro-Slutsky matrix, and the Le Chatelier-Samuelson principle, without relying on implausibly strong rationality assumptions over individual microeconomic agents. 2) the approach generates new results, including implications for money flow and trade when two or more economies are put in contact, in terms of new concepts such as economic entropy, economic temperature, goods' values and money capacity. Some of these are related to standard economic concepts (eg marginal utility of money, market prices). Yet our approach derives them at a purely macroeconomic level and gives them a meaning independent of usual restrictions. Others of the concepts, such as economic entropy and temperature, have no direct counterparts in standard economics, but they have important economic interpretations and implications, as aggregate utility and the inverse marginal aggregate utility of money, respectively. 3) this analysis promises to open up new frontiers in macroeconomics by building a bridge to ideas from non-equilibrium thermodynamics. More broadly, we hope that the economic analogue of entropy (governing the possible transitions between states of economic systems) may prove to be as fruitful for the social sciences as entropy has been in the natural sciences.

Figures

Figures reproduced from arXiv: 2412.00886 by the authors.

Figure 1
Figure 1. Sketch proof of existence of entropy: given X0, X1 as in A14, we draw the straight line of convex combinations in the space of product systems and deduce that any X between them in the accessibility order is equivalent to one point on the line; the resulting λ is the desired entropy. Here we make the natural identifications X0 ∼ (0X1, X0), X1 ∼ (X1, 0X0), X ∼ (λX,(1 − λ)X). Changing the choice of X0 ≺ X1 makes an o-… view at source ↗
Figure 2
Figure 2. Boundary of accessible region for a two-part Cobb-Douglas economy from an initial endowment (anywhere on the displayed surface). The accessible region is to the right. The economies have numbers of agents in the ratio N1 : N2 = 1 : 2, and the same exponents α = 1, η = 5 2 . The total goods G = 30. To illustrate the consequences of entropy, [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. shows contours of the entropy for the division of goods and money between two Cobb-Douglas economies with no external trader. The allowed transitions are those that do not decrease the total entropy. 0 5 10 15 20 25 30 0.0 0.2 0.4 0.6 0.8 1.0 G1 M1 S 5 10 15 20 25 30 35 40 45 [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The intersection of surfaces of constant entropy for the two economies. This intersection lies in the surface of constant total entropy shown in [PITH_FULL_IMAGE:figures/full_fig_p027_4.png]
Figure 5
Figure 5. Figure 5: An economic Carnot cycle in the plane of amount G of goods and temperature T for an island economy with α = 2, η = 5/2 operating between two mainland economies at temperatures TH = 0.47 and TC = 0.24. The nett effect of each cycle is to take some money from H and distr…
Figure 6
Figure 6. Figure 6: Carnot cycle replotted in the planes of (a) amount G of goods and price µ, (b) entropy S and temperature T. More generally, in a cyclic process, the money a trader can extract per cycle with reversible moves is the area of the loop in the (S, T)-plane, as in [PITH_FUL…
Figure 7
Figure 7. Figure 7: (a) Edgeworth box plot for the two Cobb-Douglas economies of [PITH_FULL_IMAGE:figures/full_fig_p030_7.png]
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p031_8.png]
Figure 9
Figure 9. Figure 9: Relationship between volume (quantity of goods) and price, with changes at a constant temperature (light lines) and entropy (heavy lines). The same graph replotted in temperature-entropy coordinates, so that the changes move the system along the lines of a grid. The am…

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  1. Convergence to equilibrium for a class of exchange economies

    math.PR 2025-06 conditional novelty 6.0 of 10

    For fully connected Cobb-Douglas exchange economies, the distribution of goods converges exponentially to the unique product-of-Dirichlet equilibrium for any initial condition.

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Works this paper leans on

15 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [1]

    [AD] Arrow KJ, Debreu G, Existence of an equilibrium for a competitive economy, Econometrica, 22(3) (1954) 265–290

    [A51] Arrow, KJ, An extension of the basic theorems of classical welfare economics, Proceedings of the second Berkeley symposium on mathematical statistics and probability, 2, 507–533, (University of California Press, 1951). [AD] Arrow KJ, Debreu G, Existence of an equilibrium for a competitive economy, Econometrica, 22(3) (1954) 265–290. [B+] Beck C, Ben...

    work page 1954

  2. [2]

    [Kr] Krugman P, https://quotefancy.com/paul-krugman-quotes

    (Elsevier, 1987), 1043–1092. [Kr] Krugman P, https://quotefancy.com/paul-krugman-quotes. [Ku] K¨ ummel R, The second law of economics (Springer,

    work page 1987

  3. [5]

    [DGMS] D¨ uring B, Georgiou N, Merino-Aceituno S, Scalas E, Continuum and thermodynamic limits for a simple random exchange model, Stoch Proc & Appln 149 (2022) 248–77

    Thermoeconomics, in: Demirel Y, Gerbaud V, Nonequilibrium Thermodynamics (Fourth Edition) (2019) 267–294. [DGMS] D¨ uring B, Georgiou N, Merino-Aceituno S, Scalas E, Continuum and thermodynamic limits for a simple random exchange model, Stoch Proc & Appln 149 (2022) 248–77. [DGS] D¨ uring B, Georgiou N, Scalas E, A Stylised Model for Wealth Distribution, ...

    work page 2019

  4. [11]

    Convergence to equilibrium for a class of exchange economies

    (Elsevier. 1976), 19–46. [LMC] Luo Y, MacKay RS, Chater N, Tests of thermal macroeconomic theory on simulated microeconomies, J Phys Complexity 6 (2025) 015008. [M11] MacKay RS, Robustness of Markov processes on large networks, J Difference Eqns & Applns 17 (2011) 1155–67. [M20] MacKay RS, Sustainable energy storage – with hot air, cold air and liquid air...

    work page Pith review arXiv 2025

  5. [69]

    [H96] Hartley JE, Retrospectives: The Origins of the Representative Agent, Journal of Economic Perspectives, 10(2) (1996) 169–177. [H55] Harsanyi JC, Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility, Jour- nal of Political Economy, 63 (1955) 309-–321 [HS] Hiura K, Sasa S, How does pressure fluctuate in equilibrium? J Stat...

    work page 1996

  6. [512]

    Ecological Economics 58(1) (2006) 160–169

    55 [SDb] Sousa T, Domingos T, Is neoclassical microeconomics formally valid? An approach based on an analogy with equilibrium thermodynamics. Ecological Economics 58(1) (2006) 160–169. [St] Starr RM, General equilibrium theory, 2nd edition (Cambridge U Press,

    work page 2006

  7. [1370]

    [LY99] Lieb EH, Yngvason J, The physics and mathematics of the second law of thermodynamics, Phys Rpts 310 (1999) 1–96

    [LY98] Lieb EH, Yngvason J, A guide to entropy and the second law of thermodynamics, Notices Am Math Soc 45 (1998) 571–81. [LY99] Lieb EH, Yngvason J, The physics and mathematics of the second law of thermodynamics, Phys Rpts 310 (1999) 1–96. [LY02] Lieb EH, Yngvason J, The mathematical structure of the second law of thermodynamics, in: Current developmen...

    work page 1998

  8. [1964]

    [GL] Godr` eche C, Luck J-M, Characterising the non-equilibrium stationary states of Ornstein-Uhlenbeck processes, J Phys A 52 (2019) 035002

    [Go] Goddard JD, The second law of thermodynamics as variation on a theme of Carath´ eodory, Proc Roy Soc A 477 (2021) 20210425. [GL] Godr` eche C, Luck J-M, Characterising the non-equilibrium stationary states of Ornstein-Uhlenbeck processes, J Phys A 52 (2019) 035002. [GG] Greenberg M, Gao HO, 25 years of random asset exchange models, Eur Phys J B 97 (2...

    work page 2021

Show all 15 references
  1. [1991]

    Mohammad-Djafari, G

    [Ja] Jaynes ET, The Gibbs Paradox, in: A. Mohammad-Djafari, G. Demoment (eds.), Maximum Entropy and Bayesian Methods (Springer, 1992). 53 [KF] Kaneko K, Furusawa C, Macroscopic theory for evolving biological systems akin to thermodynamics, Ann Rev Biophys 47 (2018) 273–90. [KM...

    2018

  2. [2005]

    [C+] Cockshott WP, Cottrell AF, Michaelson GJ, Wright IP, Yakovenko VM, Classical econophysics (Rout- ledge, 2009)

    [CEE] Christiano LJ, Eichenbaum M, Evans CL, Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy, J Political Economy 113(1) (2005) 1–45. [C+] Cockshott WP, Cottrell AF, Michaelson GJ, Wright IP, Yakovenko VM, Classical econophysics (Rout- ledge, 2009). [C...

    2005 arXiv

  3. [2006]

    [SST] Silver J, Slud E, Takamoto K, Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences, J Econ Theory 106 (2002) 417–435

    [Set] Sethna J, Statistical mechanics: entropy, order parameters and complexity, 2nd ed (OUP, 2021). [SST] Silver J, Slud E, Takamoto K, Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences, J Econ Theory 106 (2002) 417–435. [Sl15] Sl...

    2002

  4. [2011]

    [KP] Kydland FE, Prescott EC, Time to build and aggregate fluctuations, Econometrica 50(6) (1982) 1345–

    1982

  5. [2012]

    American Economic Review 94(4) (2004) 1014–1033

    [Su04] Sugden R, The opportunity criterion: consumer sovereignty without the assumption of coherent pref- erences. American Economic Review 94(4) (2004) 1014–1033. [Su] Sugden R, The community of advantage: A behavioural economist’s defence of the market. (Oxford University Pr...

    2004

  6. [2014]

    [Wa] Walters P, An introduction to ergodic theory (Springer, 1982)

    [Vl] Vlaev I, Seymour B, Dolan RJ, Chater N, The price of pain and the value of suffering, Psychological Science 20 (2009) 309–317. [Wa] Walters P, An introduction to ergodic theory (Springer, 1982). [Wr] Wright P, A simple piston problem in one dimension, Nonlinearity 19 (200...

    2009 arXiv

  7. [2025]

    [Gab09] Gabaix, X, Power laws in economics and finance, Annual Review of Economics, 1 (2009): 255-93

    [Ga] Gal ` ı J, Monetary policy, inflation and the business cycle (Princeton Univ Press, 2015). [Gab09] Gabaix, X, Power laws in economics and finance, Annual Review of Economics, 1 (2009): 255-93. [Gab20] Gabaix, X, A Behavioral New Keynesian Model, American Economic Review 1...

    2009

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.