You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'Foundations of equilibrium thermodynamics are the equation of state (EoS) and four postulated laws of thermodynamics. We use equilibrium thermodynamics paradigms in constructing the EoS for microeconomics system that is a market. This speculation is hoped to be first step towards whole pictures of thermodynamical paradigm of economics.'
address:
- |
    The Institute for Fundamental Study “The Tah Poe Academia Institute",\
    Naresuan University, Phitsanulok 65000, Thailand
- 'Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400, Thailand'
- |
    Graduate School of Development Economics,\
    National Institute of Development Administration (NIDA), Bangkok 10240, Thailand
author:
- Burin Gumjudpai
title: |
    Towards equation of state for a market:\
    A thermodynamical paradigm of economics
---

Introduction {#Section:Introduction}
============

Paradigms of thermostatics - a subject widely known as equilibrium thermodynamics, is very different from the rest of physics. It is reasonable to classify physics into two branches. The first one is the concept of equation of motion (EoM) which can be derived from least action principle. Integrations of the postulated Lagrangian over time or spacetime (in field theory) is the action varied to obtain the Euler-Lagrange equation - the EoM, of which generalized coordinates and generalized momenta are natural dynamical variables. The other one is the concept of equation of state (EoS) in thermostatics. The EoS is constructed not theoretically like the EoM but empirically. Manifold space variables are thermodynamic coordinates such as pressure, volume, temperature, etc. without concept of time or action. We refer to the first branch as [*dynamical laws*]{}[^1] and the second one as [*thermostatics*]{}[^2]. Considering simplest hydrostatics system, mechanical intensive coordinate ($Y$) is the minus sign of pressure ($-P$), mechanical extensive coordinate $X$ is volume ($V$), thermal intensive coordinate is temperature ($T$) and thermal extensive coordinate is entropy ($S$). Work term, $\delta W = -P\d V$ is a combination of $P$ and $V$, dubbed the [*mechanical pair*]{}. Heat term ($\delta \mathcal{Q} = T \d S$ is of the same spirit of the mechanical pair. Postulates of thermodynamics define $T$ (in the $0^{\text{th}}$ law), internal energy $U$ (in the $1^{\text{st}}$ law) and $S$ (in the $2^{\text{nd}}$ law). Constraint surface, $\Sigma$ is the EoS in form of function $f(X, Y, T)  = 0$, whereas $f(V, P, T)  = 0$ for hydrostatics system. This 4-dimensional space ($T,S,P,V$) is hence constrained into 3-dimensional space ($V, P, T$), ($V, P, S$), ($P, T, S$) or ($V, T, S$). Existence of the surface $\Sigma$ (the EoS), a 2-dimensional geometrical object described by 3 coordinates, enables one to define a thermodynamic potential function $U$ according to the Carathéodory’s theorem (see e.g. [@buchdahl; @munster]). It has been noticed that mathematics of economics equilibrium has lots of similarities to thermostatics[^3]. Previous investigation of this analogous begins with initial setup from macroeconomics [@mim] or with consideration of utility function as a thermodynamics potential [@saslow]. Here alternatively we start from the Carathéodory’s axiom since, according to the axiom, the potential is to exist as the surface $\Sigma$ exists. Hence in our setup, deriving EoS of an economics system, i.e. a market, is a key foundation of our paradigm.

The zeroth law of thermodynamical paradigm of economics
=======================================================

We assume there exists a 2-dimensional $\Sigma$ surface for a system which is a market, taking into account that three coordinates are quantities of demand ($Q^{\rm d}$), supply ($Q^{\rm s}$) and price ($Pr$). Price and temperature are both fundamentally postulated to exist before constructing theories of the subjects [@debrue]. Price is defined from market equilibrium[^4] as such the temperature is defined from thermal equilibrium. The zeroth law of thermodynamical paradigm of microeconomics should lay foundation of the concepts of market equilibrium and of price[^5]. The statement may read

> [*For three efficient, perfect competitive and clearing markets A, B, C in which there are trading of the same and homogenous normal goods. If A is in equilibrium with B and B is in equilibrium with C, hence A is in equilibrium with C. The equilibrium gives rise to existence of price function which can be ranked from lower to higher and is the character of market that determines if the market is in equilibrium with others. This type of equilibrium is the price equilibrium.*]{}[^6]

Market with $Q^{\rm d}$ and $Q^{\rm s}$ linear with price {#sec_linlin}
=========================================================

In a market, if the demand curve is of a function (referred to standard text books e.g. [@robin]), Q\^[d]{} = k\_[s]{}(Q\^[s]{})Pr + Q\^[d, 0]{} , \[eq1\] as in figure \[fig1\]. The proportional constant is $k_{\rm s}(Q^{\rm s}) < 0$ and the vertical intercept is $Q^{\rm d, 0}$. It could be elastic, unitary or inelastic demand depending on which section of the curve we consider. The supply curve is $
Q^{\rm s} = k_{\rm d}(Q^{\rm d})\cdot Pr
$ as in figure \[fig1\]. In the same spirit with the way ideal gas law is formulated, there should be a relation $Q^{\rm d} = k_{\rm Pr}(Pr)\cdot Q^{\rm s}$. Working with these relations, one finds $(Q^{\rm d})^2 = \varepsilon_{\rm d}^2 \cdot Pr^2  +  k_{\rm d} k_{\rm Pr} \cdot Pr\cdot Q^{\rm d, 0} $ where $\varepsilon_{\rm d}^2 = k_{\rm d} k_{\rm s} k_{\rm Pr} $ and that $(Q^{\rm s})^2 = \varepsilon_{\rm s}^2 \cdot Pr^2  +  ({k_{\rm d}}/{k_{\rm Pr}}) \cdot Pr \cdot Q^{\rm d, 0}   $ where $\varepsilon_{\rm s}^2 = \l(k_{\rm d} k_{\rm s}/k_{\rm Pr}\r) $. Point-price elasticity of demand and supply are E\_[d]{} = , E\_[s]{} = . \[eq2\] Since $k_{\rm s} < 0$ hence $\varepsilon_{\rm d}$ and $\varepsilon_{\rm s}$ are imaginary. At market clearing price, $Q^{\rm d} = Q^{\rm s}$, making $k_{\rm Pr} =1 $. The slope $\varepsilon_{\rm d} = \Delta Q^{\rm d}/\Delta Pr = E_{\rm d} Q^{\rm d}_0/Pr_0 = k_{\rm s} < 0$ in this case. The $\varepsilon_{\rm d}, \varepsilon_{\rm s}$ hence take both imaginary and real values. The inconsistency comes from existence of vertical intercept $Q^{\rm d, 0}$ in equation (\[eq1\]) but no vertical intercept in $
Q^{\rm s} = k_{\rm d}(Q^{\rm d})\cdot Pr
$ and from that the slope $k_{\rm d}$ and $k_{\rm s}$ are forced to be equal by market clearing condition, $Q^{\rm d} = Q^{\rm s}$.

![\[fig1\] (a) linear price demand curve (b) linear price supply curve](Fig1comb.eps){width="18pc"}

Market with unitary price demand and $Q^{\rm s}$ linear with price
==================================================================

In distinct from Sec. \[sec\_linlin\], the only change is the demand function, Q\^[d]{} = k\_[s]{}(Q\^[s]{}) , \[eq3\] as in figure \[fig2\]. Hence $k_{\rm s} > 0$ here. Note that, $\delta Q^{\rm d}  =  k_{\rm s}\cdot \delta (Pr^{-1})$ hence slope of the hyperbolic curve is $\varepsilon_{\rm d} \equiv \delta Q^{\rm d}/\delta Pr  = - k_{\rm s}/Pr^2  $. Using this slope and equation (\[eq3\]) in equation (\[eq2\]) resulting $E_{\rm d}  =  -1$ (i.e. unitary) at any points. Following similar procedure of Sec. \[sec\_linlin\], we find, $ Q^{\rm d}  = \sqrt{(k_{\rm s} k_{\rm Pr}/k_{\rm d})} Q^{\rm s}/ Pr $. Notice that the slope of supply curve is $k_{\rm d} = \varepsilon_{\rm s} = \Delta Q^{\rm s}/ \Delta Pr = E_{\rm s} Q^{\rm s}_0/Pr_{0}$. In thermostatics, the influence (mechanical force) term is an intensive variable. We shall modify the definition of $Q^{\rm d}$ to its intensive quantity that is [*price demand per household*]{}, $q^{\rm d} = Q^{\rm d}/N$, where $N$ is number of household buyers. Redefining $q^{\rm d} = k_{\rm s}\cdot (1/Pr)$ and $q^{\rm d} = k_{\rm Pr} \cdot Q^{\rm s}$, we see that $k_{\rm Pr}$ is a constant $N^{-1}$. We hence succeed in writing $f(X, Y, T) = 0$ as f(Q\^[s]{}, q\^[d]{}, Pr) = 0 q\^[d]{} = K Q\^[s]{} = q\^[d]{} Pr \[eqeos\] where $K \equiv \sqrt{k_{\rm s}/(\varepsilon_{\rm s} N)}$ playing similar role to the gas constant $R$ or $k_{\rm B}$ combining with the specific property, e.g. compressibility factor $Z(T)$ in real virial gas. Figure \[fig3\] presents analogous surface of ideal gas EoS and $f(Q^{\rm s}, q^{\rm d}, Pr)  = 0$ as $X \equiv Q^{\rm s}, Y \equiv q^{\rm d}$ and $T \equiv Pr$.

![\[fig2\] (a) unitary price demand: curve $Q^{\rm d}$ versus $Pr$ is hyperbolic. The hyperbolic slope is $\varepsilon_{\rm d} = \varepsilon_{\rm d}(Pr)$. The curve $Q^{\rm d}$ versus $1/Pr$ is linear. Price elasticity of demand is $E_{\rm d} = -1$ everywhere. (b) linear price supply curve ](Fig2comb.eps){width="23pc"}

![\[fig3\] (a) EoS of ideal gas as a 2-dim. surface (b) surface $f(Q^{\rm s}, q^{\rm d}, Pr) = 0$ (equation (\[eqeos\])) which could be EoS of market with unitary price elastics of demand.](Fig3.eps){width="12pc"}

Conclusion and critics
======================

This work attempts to find thermodynamical coordinates of a market. We propose the zeroth law such that the price plays the role of temperature. The EoS coordinates ($Q^{\rm s}, Q^{\rm d}, Pr$) are hypothesized. Market with linear price elasticity of demand is inconsistent due to market clearing (equilibrium) condition and form of equation. Inconsistency of $\varepsilon$ comes from the need that $Q^{\rm d} = Q^{\rm s}$ whiles having two different values of slope, $k_{\rm d}, k_{\rm s}$. In case of market with unitary price elasticity of demand, it is possible to derive a constraint surface with an additional idea that the demand is considered to be intensive. Validity of this EoS is still our ongoing speculation.

We notice that as we consider equilibrium state, quantity of goods in transaction should be denoted with only one single variable, $Q$, not to be considered separately as two forces of willing to sell and of willing to buy. As a result, one can not draw a set of [*isoprice curves*]{} in the same spirit as isothermal curves (see figure \[fig4\]). One of these variables might not be the correct coordinate. It is also noticed that thermal equilibrium is established in conservation condition. There are internal (the system) and external (the environment) parts to exchange heat and work hence resulting change in internal energy. The situation of market case is different. Transactions to form clearing price in a market are done by buyers and sellers who are both internal agents. Forming an equilibrium price does not tell us the total wealth of the market while forming an equilibrium temperature does tell us how much internal energy the system possesses.

We also notice that in $(P, V, T)$ system, $P$ results in change of $V$. Both are different quantities. In simple paramagnetics, magnetic field, $B_0$ induces changes in magnetization $\mathcal{M}$, via the EoS, $\mathcal{M} =  (\mathcal{D}/\mu_0) (B_0/T) $. The physical quantities $B_0$ and $\mathcal{M}$ are similar in nature. Effect of $B_0$ is [*amplified*]{} by factor $\mathcal{D}$ (Curie constant) to induce $\mathcal{M}$. In unitary market, intensive influence $q^{\rm d}$ is similar to $Q^{\rm s}$ by nature of their physical quantities. From equation (\[eqeos\]), $(1/K)$ looks like the amplification factor for $q^{\rm d}$ to induce $Q^{\rm s}$. Here we have explored possibility towards construction of an EoS for a market. We gain some insights and learn some shortcomings of the paradigm developed here to proceed in future construction of thermodynamical paradigm of economics.

![\[fig4\] (a) $T$ is an exogenous variable of the $VP$ plane. (b) In unitary demand market, $Pr$ is an exogenous however different prices do not give different curves but instead giving different value of $Q^{\rm s} = Q^{\rm d}$ via $q^{\rm d} = (1/N)Q^{\rm s}$. This is distinct from that of hydrostatics system where $P$ and $V$ are hyperbolic to each other.](Fig4.eps){width="14pc"}

Acknowledgements {#acknowledgements .unnumbered}
================

The author thanks Y. Setthapramote (NIDA) for discussion and S. Saichaemchan for the figures. The work is supported by Naresuan University Research Grant (R2557C002).

References {#references .unnumbered}
==========

[9]{}

Buchdahl H 1966 The Concepts of Classical Thermodynamics (Cambridge: Cambridge University Press) Münster A 1970 Classical Thermodynamics (Bristol: Wiley-Interscience)

Samuelson P 1990 Proc. Gibbs Symposium, ed G Caldi and G Mostow (Providence, R.I.: American Mathematical Society) p 255 Jenkins A 2005 arXiv:cond-mat/0503308 Rosser Jr J 2016 [*Eur. Phys.*]{} J [**225**]{} 3091 Mimkes J 2006 [Econophysics and Sociophysics: Trends and Perspectives]{} ed B Chakrabarti, A Chakraborti and A Chatterjee (Weinheim: Wiley-VCH) chapter 1 pp 1-34 Saslow W 1999 [*Am. J. Phys.*]{} [**67**]{} 12

Debrue G 1972 Theory of Value (New Haven: Yale University Press) Pindyck R and Rubinfeld D 2012 Microeconomics 8th Ed (London: Pearson)

[^1]: This includes all quantum physics, electrodynamics and gravitational theories.

[^2]: This is yet to include statistical mechanics and non-equilibrium thermodynamics into this consideration.

[^3]: Although mathematical isomorphism between thermostatics and macroeconomics (neoclassical theory) was accepted by Samuelson but he did not accept that there are exact analogies of physical magnitudes in the economics realm [@sam]. A macroeconomic system inevitably relies on the concept of entropy and indeed economics system is driven by entropy (see e.g. [@jk; @rosser]).

[^4]: a condition when there is no excessive demand or excessive supply

[^5]: Note that mechanism of thermal and market equilibrium formations are quite different and this is to be discussed in future work.

[^6]: There are other types of economics equilibrium such as interest rate equilibrium and exchange rate equilibrium.