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<p class="tagline" role="doc-subtitle">Public proof artifact · credit structure and reviewable monitoring</p>
<p class="muted" style="margin:6px 0 10px">This page shows how Toppy frames complex economic monitoring work: explicit assumptions, inspectable mappings, and public artifacts that can be challenged rather than merely asserted.</p>
<h1>Thermo-Credit theory: credit structure, capacity, and reviewable monitoring</h1>
<p class="muted">QTC stands for Quantity Theory of Credit. The aim is to make credit capacity and allocation structure explicit, rather than treating money aggregates alone as the main object of analysis.</p>
<p class="muted">The thermodynamics language used here is an <strong>analytic bookkeeping correspondence</strong> for decision support, not a claim that economies literally obey physical law. What matters is whether the definitions, state variables, and indicators are explicit enough to inspect, test, and falsify.</p>
<p style="margin:12px 0 0">
<a class="btn" href="https://doi.org/10.5281/zenodo.17778342" target="_blank" rel="noopener noreferrer">Download technical note (Zenodo)</a>
</p>
<section class="callout" id="key-links" style="margin-top:12px">
<h2 class="section-caption">Key links</h2>
<div style="display:flex; gap:10px; flex-wrap:wrap; margin-top:6px">
<a class="btn" href="https://doi.org/10.5281/zenodo.17778342" target="_blank" rel="noopener noreferrer">Zenodo record (PDF + source)</a>
<a class="btn" href="https://www.toppymicros.com/2025_11_Thermo_Credit/report.html" target="_blank" rel="noopener noreferrer">Open dashboard report</a>
<a class="btn" href="https://github.com/ToppyMicroServices/2025_11_Thermo_Credit" target="_blank" rel="noopener noreferrer">GitHub repo</a>
</div>
<div style="margin-top:10px">
<div><strong>What you get</strong></div>
<ul style="margin:6px 0 0 18px">
<li>A plain-English mapping of QTC to thermodynamics-style concepts with clear definitions.</li>
<li>A correspondence table with compact notes for fast inspection.</li>
<li>A reproducible report and monitoring view for early-warning work.</li>
</ul>
</div>
</section>
<section class="card" id="abstract" style="margin-top:12px">
<h2>Plain-English abstract</h2>
<p><strong>Thermo-Credit Theory</strong> reinterprets the Quantity Theory of Credit (QTC) through the lens of thermodynamics. It treats <strong>credit expansion and repayment</strong> as energy-like flows within a financial system that has measurable capacity, pressure, and dispersion. This mapping is not physics—it is a structured bookkeeping analogy designed for decision support and early-warning analytics.</p>
<p>QTC extends the classic <strong>Quantity Theory of Money (QTM)</strong> by adding an explicit capacity term, \(V_C\), for the banking system. Just as physical systems have pressure–volume interactions, credit systems respond to changes in balance-sheet headroom and regulatory constraints. This allows us to separate random liquidity diffusion from intentional policy work, and to test whether data behave like state variables.</p>
<p>The theory introduces <strong>entropy-like dispersion</strong>, <strong>credit potential</strong>, and <strong>free-energy measures</strong> (\(F_C, X_C\)) to monitor stress and policy space. These quantities can be calculated from public balance-sheet and market data, producing falsifiable indicators. <strong>Thermo-Credit</strong> therefore serves as both a conceptual bridge between money and information, and a practical framework for quantitative supervision.</p>
</section>
</header>
<main>
<!-- Page structure: TOC block -->
<!-- Table of contents -->
<section class="toc" aria-label="Table of contents">
<strong>Contents</strong>
<ol>
<li><a href="#plain-en">Plain-English summary</a></li>
<li><a href="#overview">Overview</a></li>
<li><a href="#correspondence">Correspondence table</a></li>
<li><a href="#bank-credit">Bank credit creation</a></li>
<li><a href="#free-vs-exergy">Free energy (F_C) & optional exergy (X_C)</a></li>
<li><a href="#maxwell">Maxwell-like relations</a></li>
<li><a href="#rephrasing">Is it merely a rephrasing?</a></li>
<li><a href="#insights">What the analogy adds (insights & tests)</a></li>
<li><a href="#limits">Limitations & scope</a></li>
<li><a href="#refs">Minimal references</a></li>
<li><a href="#disclaimer">Disclaimer & status</a></li>
<li><a href="#app">App behavior</a></li>
</ol>
<div class="muted" style="margin-top:6px">Recommended reading order: <a href="#plain-en">Plain-English summary</a> → <a href="#correspondence">Correspondence table</a> → <a href="#bank-credit">Bank credit creation</a> → <a href="#insights">Insights & tests</a>.</div>
<div class="muted" style="margin-top:6px">Key equations: <a href="#eq1" class="eqref">(1)</a> <a href="#eq2" class="eqref">(2)</a> <a href="#eq3" class="eqref">(3)</a> <a href="#eq4" class="eqref">(4)</a> <a href="#eq5" class="eqref">(5)</a></div>
</section>
<section id="plain-en" class="card" style="margin-top:12px">
<h2>Plain-English summary (QTM vs QTC & the first/second laws)</h2>
<p><strong>What we compare.</strong> Two stories about money/credit: the classic Quantity Theory of Money (QTM) [3,4,6] and Werner’s Quantity Theory of Credit (QTC) [9].</p>
<ul>
<li><strong>QTM — Quantity Theory of Money (money-first):</strong> more money → higher prices, if money moves fast enough.</li>
<li><strong>QTC — Quantity Theory of Credit (credit-first) [9]:</strong> banks create deposits when they lend; what credit is used for matters.</li>
</ul>
<p><strong>First law (bookkeeping idea).</strong></p>
<ul>
<li><strong>QTM:</strong> in the classic quantity-theory view [3, 4, 6], changes are explained via money stock, velocity, and policy shocks, without an explicit “capacity” state variable. Here we restate that as a split between (a) policy work and (b) extra mixing of money across uses.</li>
<li><strong>QTC:</strong> same split, but now we also track <em>capacity/headroom</em> on bank balance sheets. Using up headroom shows up like a pressure × volume term (work from constraints).</li>
</ul>
<p><strong>Second law (one-way tendency).</strong></p>
<ul>
<li><strong>Both:</strong> random mixing tends to raise our entropy-like index. To reverse it (make it more concentrated) you need structure—policy, rules, guidance.</li>
<li><strong>Only in QTC:</strong> tightening or relaxing capacity shifts the “pressure” of constraints, which changes how hard it is to concentrate or relax the system.</li>
</ul>
<p><strong>Why QTC adds value.</strong> QTC makes the hidden capacity/pressure channel explicit. That lets us distinguish “more random dispersion” from “intentional work by policy or rules” — which is exactly what you want for audit trails and early-warning dashboards.</p>
</section>
<!-- Primer -->
<!-- Overview -->
<section id="overview" class="card" style="margin-top:12px">
<h2>Overview</h2>
The index we informally described above is made precise as follows.
<p><span class="def-label">Definition.</span> Monetary dispersion entropy (entropy-like, extensive):
<span id="eq1"></span>
\[
S_M \;=\; k\,M_{\mathrm{in}}\,H(q),\quad H(q)\equiv -\sum_i q_i\,\log q_i \tag{1}
\]
where <code>M_in</code> is the actual money-in-circulation over a chosen period/system and <code>q</code> are composition shares (MECE, stable).</p>
<p class="muted">Entropy form follows Shannon [12]. Economic applications of entropy/dispersion include Theil’s information-theoretic index [7]. We map ideal mixing \(\Delta S_{mix}=k_B N H(x)\) to money shares \(q\) and scale \(M_{in}\).</p>
</section>
<!-- Correspondence -->
<section id="correspondence" class="card tight-math" style="margin-top:12px">
<h2>Correspondence table</h2>
<p class="muted">Thermodynamics column is literal; QTM/QTC columns are analogy-level correspondences. Heat/Work entries are “-like” bookkeeping splits, not physical identities.</p>
<p class="muted">Notes are hidden behind the ⓘ icons; hover (or tap) to read.</p>
<table class="qtmqtc">
<colgroup>
<col style="width: 12rem">
<col style="width: 14rem"><!-- Thermodynamics slightly wider to avoid overlap -->
<col style="width: 15rem"><!-- QTM -->
<col style="width: 16rem"><!-- QTC -->
<col style="width: auto"><!-- Notes -->
</colgroup>
<thead>
<tr>
<th> Variable </th>
<th>Thermodynamics</th>
<th>QTM (money-first)</th>
<th>QTC (credit-first)</th>
<th>Notes</th>
</tr>
</thead>
<tbody>
<tr>
<td > Mixing entropy </td>
<td>\(\Delta S_{mix}=k_B N H(x)\)</td>
<td>\( S_M = k\,M_{in}\,H(q) \)</td>
<td>\( S_M = k\,M_{in}\,H(q) \)</td>
<td class="notes-cell" data-note="Same form (scale × dispersion). Both use money-in-circulation and shares; QTC later links it to capacity."></td>
</tr>
<tr>
<td>Temperature</td>
<td>\( T \)</td>
<td> \( T_L \) </td>
<td> \( T_L \) </td>
<td class="notes-cell" data-note="In both QTM/QTC, temperature stands for a liquidity proxy."></td>
</tr>
<tr>
<td>Internal energy</td>
<td>\( U \)</td>
<td> \( U_M(S_M) \)</td>
<td> \( U(S_M,V_C,\dots) \)</td>
<td class="notes-cell" data-note="QTM omits explicit capacity. QTC treats U as a credit potential in (S_M, V_C)."></td>
</tr>
<tr>
<td>Volume</td>
<td>\( V \)</td>
<td>—</td>
<td>\( V_C \)</td>
<td class="notes-cell" data-note="QTM: no explicit capacity variable (often absorbed into velocity). QTC: explicit capacity V_C with headroom separated."></td>
</tr>
<tr>
<td>Pressure</td>
<td>\( p \)</td>
<td>—</td>
<td>\( p_C \equiv -\,(\partial U/\partial V_C)_{S_M} \)</td>
<td class="notes-cell" data-note="QTM: no pressure term. QTC: credit pressure p_C (shadow price of capacity) appears only in QTC."></td>
</tr>
<tr>
<td>Heat (heat-like)</td>
<td>\( \delta Q_{\mathrm{rev}} = T\,dS \)</td>
<td>\( Q_M \sim T_0\,\Delta S_M \)</td>
<td>\( Q_C \sim \bar T_L\,\Delta S_M \)</td>
<td class="notes-cell" data-note="Heat-like mixing term. QTM/QTC use T_0 or liquidity T̄_L times dispersion change; not literal physical heat."></td>
</tr>
<tr>
<td>Work (work-like)</td>
<td>\( \delta W = p\,dV \)</td>
<td>\( W_M \equiv W_{\mathrm{policy}} \)</td>
<td>\( W_C \equiv -\,\bar p_C\,\Delta V_C \;+\; W_{\mathrm{policy}} \)</td>
<td class="notes-cell" data-note="Work-like structured term. QTM: policy work only. QTC: constraint work -p̄_C ΔV_C plus policy work; analogy to p dV."></td>
</tr>
<tr>
<td>First law </td>
<td>
<span class="stack-eq">\( \Delta U \equiv T\,\Delta S + W \)</span>
</td>
<td>\( \Delta U_M = T_0\,\Delta S_M + W + \varepsilon \)</td>
<td>\( \Delta U = \bar T_L\,\Delta S_M + W + \varepsilon \)</td>
<td class="notes-cell" data-note="Unified bookkeeping: W collects work-like contributions. QTM: W = W_policy. QTC: W = W_C = -p̄_C ΔV_C + W_policy. Analogy-level, not a physical identity."></td>
</tr>
<tr>
<td>Second law (monotonicity)</td>
<td>\( \Delta S \ge 0 \) </td>
<td>\( \Delta S_M \ge 0 \)</td>
<td>\( \Delta S_M \ge 0 \)</td>
<td class="notes-cell" data-note=" Random mixing raises the dispersion index; concentration (ΔS_M < 0) requires structured work/policy. This is an entropy-like tendency, not a strict physical second law."></td>
</tr>
<tr>
<td>Helmholtz free energy</td><td>\( F \)</td>
<td>\( F_M \equiv U_M - T_0 S_M \)</td>
<td>\( F_C \equiv U - T_0 S_M \)</td>
<td class="notes-cell" data-note="Early-warning gauge under fixed environment; QTC also allows Gibbs/exergy variants."></td>
</tr>
<tr>
<td>Exergy / availability</td>
<td>\( X \)</td>
<td>\(X_M \approx U_M - T_0 S_M\)</td>
<td>\( X_C = \Delta U + p_0\Delta V_C - T_0 \Delta S_M \)</td>
<td class="notes-cell" data-note="Boundary-dependent; p_0 term requires an explicit capacity variable (QTC). In QTM, exergy lacks the p_0 term."></td>
</tr>
</tbody>
</table>
<div class="small-print muted" style="margin-top:8px" aria-label="Footnote: meaning of U in QTM/QTC">
<strong>Note — What does <em>U</em> mean here?</strong>
<ul style="margin:6px 0 0 16px">
<li><strong>QTM:</strong> <em>Bookkeeping potential</em> \(U_M(S_M)\) so that a first‑law‑like split holds: \(\Delta U_M = T_0\,\Delta S_M + W_{policy} + \varepsilon\). Not a standard variable in classic QTM.</li>
<li><strong>QTC:</strong> <em>Credit state potential</em> \(U(S_M,V_C,\dots)\) with conjugates \(T_L=(\partial U/\partial S_M)_{V_C}\), \(p_C=-(\partial U/\partial V_C)_{S_M}\).</li>
</ul>
<span>We use \(U\) as an analytic device; original QTM/QTC do not name \(U\).</span>
</div>
</section>
<!-- Laws & Carnot bound -->
<!-- Bank credit creation (moved above Free energy & Maxwell) -->
<section id="bank-credit" class="card" style="margin-top:12px">
<h2>Bank credit creation (within this mapping)</h2>
<h3>Balance-sheet identity (loans create deposits)</h3>
<p>When a bank grants a new loan, it books the loan as an asset and simultaneously creates a matching deposit as a liability. On the customer side, the new deposit is an asset and the loan is a liability. This standard identity is the only accounting ingredient we need.</p>
<span id="eq2"></span>
\[
\Delta U \;\approx\; \bar T_L\,\Delta S_M \;-
\; \bar p_C\,\Delta V_C \;+
\; W_{\mathrm{policy}} \;+
\; \varepsilon \tag{2}
\]
<p class="small-print muted" style="margin-top:-4px;margin-bottom:8px">This expresses the <strong>credit‑creation energy balance</strong> — the “ΔU of credit creation,” decomposing changes into liquidity (T̄<sub>L</sub> ΔS<sub>M</sub>), capacity (−p̄<sub>C</sub> ΔV<sub>C</sub>), and policy work (W<sub>policy</sub>).</p>
<ul>
<li><strong>\( \Delta S_M \)</strong>: with \( S_M = k\,M_{\mathrm{in}}\,H(q) \), credit creation typically raises \( M_{\mathrm{in}} \) (scale term) and, via allocation changes, may alter \( H(q) \), pushing \( S_M \) upward.</li>
<li><strong>\( \Delta V_C \)</strong>: new lending <em>uses</em> headroom so \( \Delta V_C < 0 \) (capacity declines). Hence the term \( -\bar p_C\, \Delta V_C > 0 \) contributes positively.</li>
<li><strong>\( W_{\mathrm{policy}} \)</strong>: includes structural work from regulation, capital injections, guarantees, purchases (QE/collateral ops), etc.</li>
</ul>
<h3>Creation vs repayment (sign conventions)</h3>
<p class="small-print muted" style="margin-top:-2px;margin-bottom:6px">Notation: \(\Delta M_{\mathrm{in}}\) = change in money-in-circulation over the period. Arrows ↑/↓ denote increase/decrease.</p>
<table>
<thead>
<tr>
<th>Variable</th>
<th>Credit creation (new lending > repayments)</th>
<th>Credit contraction (repayments > new lending)</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(\Delta M_{\mathrm{in}}\)</td>
<td>> 0</td>
<td>< 0</td>
</tr>
<tr>
<td>\(\Delta S_M\)</td>
<td>increase (scale ↑; dispersion may also rise)</td>
<td>decrease (scale ↓; if concentration increases, fall is larger)</td>
</tr>
<tr>
<td>\(\Delta V_C\)</td>
<td>\(< 0\) (headroom used)</td>
<td>\(> 0\) (headroom restored)</td>
</tr>
<tr>
<td>\(-\,\bar p_C\, \Delta V_C\)</td>
<td>> 0</td>
<td>< 0</td>
</tr>
<tr>
<td>\(\Delta F_C = \Delta(U - T_0 S_M)\)</td>
<td>sign depends on \(T_0\), dispersion changes, and \(p_C\)</td>
<td>same (case by case)</td>
</tr>
</tbody>
</table>
<h3>Measurement proxies (practical)</h3>
<ul>
<li><strong>Credit flows/stocks</strong>: new loans, margin/credit for securities, corporate bonds/CP issuance (use stock series differences if needed).</li>
<li><strong>Shares \(q\)</strong>: use a stable MECE partition by use/sector/instrument and update monthly.</li>
<li><strong>Capacity \(V_C\)</strong>: CET1/RWA headroom, LCR/NSFR slack, HQLA-based lending capacity.</li>
<li><strong>Temperature \(T_L\)</strong>: composite intensity index from spreads, turnover, and order-book depth (z-scored).</li>
<li><strong>Pressure \(p_C\)</strong>: estimate via \(p_C \approx -\Delta U/\Delta V_C\) regressions or policy-shock differences.</li>
</ul>
<h3>Monthly algorithm (implementation steps)</h3>
<ol>
<li>Aggregate credit flows/stocks \(f_i\); compute shares as \(q_i = f_i/\sum_i f_i\).</li>
<li>Observe \(M_{\mathrm{in}}\) and compute \(S_M = k\,M_{\mathrm{in}}\,H(q)\).</li>
<li>Build \(V_C\) from RWA, LCR/NSFR, and HQLA metrics.</li>
<li>Compute \(T_L\) from market microstructure (spreads/turnover/depth).</li>
<li>Evaluate \(\Delta U = \bar T_L \Delta S_M - \bar p_C \Delta V_C + W_{policy} + \varepsilon\).</li>
<li>Detect events: label months with \(\Delta M_{\mathrm{in}}\) spikes (or net credit inflow if available) as credit-creation periods and decompose contributions.</li>
</ol>
</section>
<!-- Inserted: Free energy (F_C) and exergy (X_C) section -->
<section id="free-vs-exergy" class="card" style="margin-top:12px">
<h2>Free energy \(F_C\) — and optional exergy \(X_C\)</h2>
<p><strong>Why this exists.</strong> We want a single scalar potential for the QTC side that (i) decreases as dispersion <em>\(S_M\)</em> increases under a fixed environment, and (ii) provides an upper bound on structured work over a cycle. A Helmholtz-style free energy plays exactly this role.</p>
<p><strong>Definition.</strong> With a state potential \(U(S_M,V_C,\dots)\) and fixed environment \(T_0\): <span id="eq3"></span>
\[
F_C \equiv U - T_0 S_M,\qquad dF_C = -\,p_C\,dV_C + \delta W_{other} \tag{3}
\]
<p>It serves as an early-warning gauge: when \(\Delta F_C \to 0\), policy headroom for structured work dries up.</p>
<details><summary class="muted">Exergy \(X_C\) (optional, environment-dependent)</summary>
<p>When an ambient pressure-like term matters, use the exergy-like availability:
<span id="eq4"></span>
\[
X_C = (U-U_0) + p_0\,(V_C - V_{C0}) - T_0\,(S_M - S_{M0}) \tag{4}
\]
<p>It reduces to \(-\Delta F_C\) if \(p_0\) effects are negligible and \(V_C\) is fixed. Because \(X_C\) depends on boundary choices \((T_0, p_0)\), we treat it as an advanced/optional metric. This Version 2 update refines the definition and boundary conditions for \(X_C\) compared to earlier drafts.</p>
</details>
<details><summary class="muted">Gibbs free energy \(G_C\) (optional, fixed \(p_0\) environment)</summary>
<p>When both temperature- and pressure-like environments are treated as fixed, the Gibbs free energy is convenient:
\[
G_C \equiv U + p_0\,V_C - T_0\,S_M,\qquad dG_C = V_C\,dp_0 - S_M\,dT_0 + \delta W_{other}
\]
In practice, we use \(F_C\) for fixed-volume analyses and \(G_C\) when an ambient pressure-like \(p_0\) is the natural control.</p>
</details>
</section>
<!-- Maxwell relations -->
<section id="maxwell" class="card" style="margin-top:12px">
<h2>Maxwell-like relations (integrability)</h2>
<p>Given the state potential \(U(S_M,V_C,\dots)\) implied by the correspondence table and the \(F_C\) definition above, mixed partials must commute, giving a Maxwell-like condition:</p>
<span id="eq5"></span>
\[
T_L = \left(\frac{\partial U}{\partial S_M}\right)_{V_C},\quad
p_C = -\left(\frac{\partial U}{\partial V_C}\right)_{S_M}
\;\Rightarrow\;
\left(\frac{\partial T_L}{\partial V_C}\right)_{S_M}
= -\left(\frac{\partial p_C}{\partial S_M}\right)_{V_C} \tag{5}
\]
<p>Violations in data falsify the mapping (i.e., chosen variables are not state-like or proxies are inadequate).</p>
</section>
<!-- Laws & Carnot bound -->
<!-- Thermodynamic laws: QTM vs QTC (side-by-side) -->
<!-- Rephrasing? -->
<section id="rephrasing" class="card" style="margin-top:12px">
<h2>Is this merely a rephrasing?</h2>
<p>Mathematically it is a change of coordinates that isolates <em>scale</em> and <em>dispersion</em>. It becomes non-trivial because it yields: (i) <strong>falsifiable integrability constraints</strong> (Maxwell-like), (ii) a <strong>clean separation</strong> of policy work vs dispersion, and (iii) an <strong>exergy/free-energy lens</strong> for early-warning ceilings via \(X_C\) or \(F_C\).</p>
</section>
<!-- Insights from the analogy -->
<section id="insights" class="card" style="margin-top:12px">
<h2>What the analogy adds (insights & tests)</h2>
<ul>
<li><strong>Integrability test (Maxwell-like):</strong> Estimate \(T_L(S_M,V_C)\), \(p_C(S_M,V_C)\); check
\((\partial T_L/\partial V_C)_{S_M} \approx - (\partial p_C/\partial S_M)_{V_C}\). Persistent failure ⇒ mapping/proxies are wrong.</li>
<li><strong>Work vs dispersion:</strong> Decompose
\(\Delta U = \bar T_L\,\Delta S_M - \bar p_C\,\Delta V_C + W_{policy}\)
to separate random mixing from structured/policy effects.</li>
<li><strong>Free-energy/exergy ceilings:</strong> Use \(F_C\) or \(X_C\) as early-warning gauges when they approach zero under chosen boundaries.</li>
<li><strong>Loop area (hysteresis):</strong> Non-zero loop area in \((p_C,V_C)\) over policy cycles measures dissipative stress.</li>
</ul>
</section>
<!-- Limitations -->
<section id="limits" class="card" style="margin-top:12px">
<h2>Limitations & scope</h2>
<ul>
<li><strong>Category dependence:</strong> \(S_M\) depends on how uses/sectors are binned; require robustness checks.</li>
<li><strong>Proxy noise:</strong> \(T_L, V_C, p_C\) are noisy proxies; mis-measurement can break Maxwell-like relations.</li>
<li><strong>Quasi-static only:</strong> Fast crises and regime shifts violate the smooth state-variable picture.</li>
<li><strong>Non-physical:</strong> No microscopic “money particles” are assumed; this is structured bookkeeping, not physics.</li>
<li><strong>Identification:</strong> Policy and shocks move terms jointly; causal claims need proper empirical design.</li>
<li><strong>Scaling conventions:</strong> Parameters like \(k\) are conventional; report normalized, sensitivity-tested metrics.</li>
<li><strong>No guarantee of physical laws.</strong> Nothing here asserts or guarantees that macro-financial data obey the physical first or second laws; all mappings are analogy-level and subject only to empirical testing.</li>
</ul>
</section>
<!-- Proxies & identification map -->
<!-- Analogy literature & conventions -->
<!-- Minimal references (selected) -->
<section id="refs" class="card" style="margin-top:12px">
<h2>Minimal references (selected)</h2>
<ul>
<li>[1] <strong>Kocherlakota, N. R.</strong> (1998). “Money is Memory.” <span class="muted">Journal of Economic Theory</span> 81(2): 232–251.</li>
<li>[2] <strong>Kocherlakota, N. R.</strong> (2002). “Money is Memory.” <span class="muted">Minneapolis Fed Quarterly Review</span> 26(1): 2–10.</li>
<li>[3] <strong>Fisher, I.</strong> (1911). <em>The Purchasing Power of Money</em>. <span class="muted">Macmillan.</span></li>
<li>[4] <strong>Friedman, M.</strong> (1956). “The Quantity Theory of Money—A Restatement.” In <em>Studies in the Quantity Theory of Money</em> (ed. Friedman). <span class="muted">University of Chicago Press.</span></li>
<li>[5] <strong>Friedman, M., & Schwartz, A. J.</strong> (1963). <em>A Monetary History of the United States, 1867–1960</em>. <span class="muted">Princeton University Press.</span></li>
<li>[6] <strong>Laidler, D.</strong> (1985, 3rd ed.). <em>The Demand for Money: Theories, Evidence, and Problems</em>. <span class="muted">Harper & Row.</span></li>
<li>[7] <strong>Theil, H.</strong> (1967). <em>Economics and Information Theory</em>. <span class="muted">North-Holland.</span></li>
<li>[8] <strong>Bank of England (McLeay, Radia, Thomas)</strong> (2014). “Money creation in the modern economy.” <span class="muted">Quarterly Bulletin.</span></li>
<li>[9] <strong>Werner, Richard A.</strong> (2011 keynote; 2012 journal; 2014 article). “Quantity Theory of Credit” program and bank money creation evidence. <span class="muted">International Review of Financial Analysis</span>.</li>
<li>[10] <strong>Borio & White</strong> (2004). “Whither monetary and financial stability?” <span class="muted">BIS Working Paper 147</span>.</li>
<li>[11] <strong>Fontana, G.</strong> (2004). “Rethinking endogenous money.” <span class="muted">Metroeconomica</span>.</li>
<li>[12] <strong>Shannon, C. E.</strong> (1948). “A Mathematical Theory of Communication.” <span class="muted">Bell System Technical Journal</span>.</li>
<li>[13] <strong>Jaynes, E. T.</strong> (1957). “Information Theory and Statistical Mechanics.” <span class="muted">Physical Review</span>.</li>
<li>[14] <strong>Callen, H. B.</strong> (1985, 2nd ed.). <em>Thermodynamics and an Introduction to Thermostatistics</em>. <span class="muted">Wiley.</span></li>
<li>[15] <strong>Zemansky, M. W., & Dittman, R. H.</strong> (1997, 7th ed.). <em>Heat and Thermodynamics</em>. <span class="muted">McGraw-Hill.</span></li>
<li>[16] <strong>Foley, D. K.</strong> (1994). “A statistical equilibrium theory of markets.” <span class="muted">Journal of Economic Theory</span>.</li>
<li>[17] <strong>Drăgulescu, A., & Yakovenko, V. M.</strong> (2000). “Statistical mechanics of money.” <span class="muted">European Physical Journal B</span>.</li>
<li>[18] <strong>Wall, G.</strong> (1977). “Exergy—a useful concept.” <span class="muted">Chalmers University preprint; later textbooks.</span></li>
</ul>
</section>
<!-- Footnotes -->
<section class="footnotes" aria-label="Footnotes">
<ol>
<li id="fn1">
<strong>Rigor & reproducibility.</strong> Text on this page was generated with a reasoning model (<em>GPT‑5 Thinking</em>) at low randomness (temperature ≈ 0.2; top‑p = 1.0). No external web browsing was used. Equations are rendered with MathJax v3 from a public CDN; minor layout differences may occur across browsers. Data outputs in <code>report.html</code> are reproducible with Python 3.11 and the packages listed in <code>requirements.txt</code>. The GitHub Actions workflow pins versions and uses <code>FRED_API_KEY</code> for online fetch, or local CSVs if not set. <span aria-hidden="true">↩</span>
</li>
</ol>
</section>
<!-- Disclaimer & status -->
<section id="disclaimer" class="card" style="margin-top:12px">
<div class="small-print">
<p><strong>Disclaimer & status.</strong> This material is part of an ongoing research program. Findings are preliminary and may change. Our approach is pragmatic and engineering-led, with priority on decision-useful results.</p>
<ul>
<li><strong>No warranties.</strong> Provided as-is without any warranty of accuracy, completeness, or fitness for a particular purpose.</li>
<li><strong>No liability.</strong> ToppyMicroServices OÜ and the authors disclaim liability for any loss or damage arising from use of this material.</li>
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<li><strong>Research only.</strong> Not an offer to sell or a solicitation to buy any security, product, or service.</li>
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<li><strong>Jurisdiction.</strong> Users are responsible for compliance with applicable local laws and regulations.</li>
<li><strong>Independence.</strong> Independent research; views are solely those of the authors.</li>
<li><strong>Forward-looking statements.</strong> Forward-looking statements are uncertain and actual outcomes may differ materially.</li>
<li><strong>Regulatory status.</strong> This content is not a regulated financial service (e.g., investment adviser, broker-dealer) and should not be treated as such.</li>
</ul>
<p class="muted">Rationale: Economics here is treated at the limit of pragmatism—tools must earn their keep in real operations before being formalized in journals. Empirical validation and falsification are ongoing.</p>
</div>
</section>
<!-- App behavior -->
<section id="app" class="card" style="margin-top:12px">
<h2>App behavior</h2>
<ul>
<li>Monthly build computes \(S_M\), \(T_L\), loop_area (PLD), and \(X_C\) from public data.</li>
<li>Interactive report (with PNG fallbacks): <a href="https://www.toppymicros.com/2025_11_Thermo_Credit/report.html" target="_blank" rel="noopener noreferrer">Open report</a></li>
<li>Repository: <a href="https://github.com/ToppyMicroServices/2025_11_Thermo_Credit" target="_blank" rel="noopener noreferrer">GitHub repo</a></li>
</ul>
</section>
</main>
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