# Entropy
<!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside -->
## Microsims — three.js
### Entropy (three.js)
<div class="microsim-player">
<iframe src="https://wikitube-3d-microsims.netlify.app/Entropy.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Entropy — three.js microsim"></iframe>
</div>
**Open it full-screen:** [Entropy.html](https://wikitube-3d-microsims.netlify.app/Entropy.html) · library `threejs` · route `microsim/threejs/`
### Related microsims
Live sims on neighbouring articles — 2 of them inside this article's own Wikipedia link tree:
- [[Binding_energy]] *(in tree)*
- [[Second_law_of_thermodynamics]] *(in tree)*
- [[Kinetic_theory_of_gases]]
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
<!-- MICROSIMGEN:END -->
## Microsim
### Live player
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/A-Lx_2q2s" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe>
</div>
<div class="microsim-fallback">
<img src="Microsims/thumbs/Entropy.png" alt="Entropy microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;">
<p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/A-Lx_2q2s">open sketch in the p5.js editor</a></em></p>
</div>
**Editor URL:** https://editor.p5js.org/sciencenibber/sketches/A-Lx_2q2s
**Description (100 words):**
The sketch demonstrates the Second Law through a two-reservoir heat exchange. The reader controls T_hot, T_cold, and the heat flux Q, then toggles between two modes: direct conduction (irreversible — all Q flows hot to cold) and a Carnot engine (reversible — engine extracts work W = (1 - T_c/T_h) Q). The top diagram shows two tanks linked by animated heat-flow tokens, with a Carnot engine box displaying the current efficiency. Below, a live scope plots three entropy stocks versus time: S_hot falling, S_cold rising, and S_univ — the sum — climbing monotonically in direct mode and flat in the reversible limit. A reset button zeroes the stocks; the bottom strip prints live dS/dt values alongside the canonical Clausius equation dS = dQ_rev / T.
```js
// =====================================================================
// Entropy.js -- Wikitube microsim
// Article: Entropy en.wikitube.io/wiki/Entropy
// Room: Helium Pattern: K (stock-and-flow,
// conservation, balance eqs)
// ---------------------------------------------------------------------
// Idea: two thermal reservoirs (hot, cold) exchange heat Q. The reader
// chooses between two modes:
//
// * direct conduction -- all Q flows hot -> cold, no work
// * Carnot engine -- engine extracts maximum work
// W = eta * Q, eta = 1 - T_c / T_h
// heat ejected to cold is Q_c = Q * T_c/T_h
//
// Three entropy stocks accumulate by forward-Euler integration:
//
// dS_hot = -Q_h / T_h (hot reservoir loses entropy)
// dS_cold = +Q_c / T_c (cold reservoir gains entropy)
// dS_univ = dS_hot + dS_cold (never decreases -- 2nd law)
//
// Clausius (1865): dS = dQ_rev / T (entropy is a state function)
// Boltzmann (1877): S = k_B ln W (statistical interpretation)
// Gibbs (1902): S = -k_B sum p_i ln p_i
// Nernst (1906): S(T -> 0) = 0 (perfect crystal, 3rd law)
// Carnot bound: equality dS_univ = 0 only in reversible limit;
// direct conduction makes dS_univ > 0 whenever
// T_h > T_c, by amount Q * (1/T_c - 1/T_h).
//
// Visual layout (720 x 520 canvas):
// y 0 - 45 HUD region (title 22pt + subtitle 12pt)
// y 50 - 190 reservoir diagram: hot tank | engine | cold tank
// with heat-flow arrows and animated tokens
// y 195 - 340 entropy scope: 3 traces vs. time
// S_hot (warm) -- falling
// S_cold (cool) -- rising
// S_univ (accent) -- monotone non-decreasing
// y 345 - 455 control panel: T_h slider, T_c slider, Q slider,
// mode toggle button, reset button
// y 460 - 510 live readout strip + canonical equations
//
// Conventions (Betterfire Standard v0, P5_JS_EDITOR section 2):
// * single ARTICLE constant at top, SINGLE QUOTES
// * p5.disableFriendlyErrors = true (keep editor console clean)
// * createCanvas(720, 520); pixelDensity(2); textFont('system-ui')
// * every createSlider has .position(x, y).size(w) -- never default
// * non-ASCII (Greek eta, lambda, dots, arrows) lives in COMMENTS
// ONLY -- text() string literals are pure ASCII so the editor
// preview pipeline never mangles a glyph
// * Energy-room palette (P5_JS_EDITOR section 4):
// BG=18 FG=240 HOT=[220,110,60] COLD=[60,130,220]
// STRUCT=[120,130,150] TRAJ=[240,220,80] GAUGE=[120,220,140]
// =====================================================================
const ARTICLE = 'Entropy';
const TITLE = ARTICLE.replace(/_/g, ' ');
p5.disableFriendlyErrors = true;
// ----- Energy-room palette ------------------------------------------
const BG = 18;
const FG = [240, 240, 240]; // array so fill(...FG) / stroke(...FG) spread
const DIM = [240, 240, 240, 140];
const HOT = [220, 110, 60];
const COLD = [60, 130, 220];
const STRUCT = [120, 130, 150];
const TRAJ = [240, 220, 80];
const GAUGE = [120, 220, 140];
const SCRATCH = [120, 120, 120, 90];
// ----- Layout regions (canvas y-coordinates) -----------------------
const TOP_Y = 50;
const TOP_H = 140;
const SCOPE_Y = 195;
const SCOPE_H = 145;
const CTRL_Y = 345;
const CTRL_H = 110;
const READOUT_Y = 460;
// ----- DOM controls ------------------------------------------------
let thSlider, tcSlider, qSlider;
let modeBtn, resetBtn;
// ----- Mode --------------------------------------------------------
// 'carnot' -- reversible engine extracts W = eta * Q
// 'direct' -- direct conduction, all Q flows hot -> cold
let mode = 'carnot';
// ----- Stocks ------------------------------------------------------
// cumulative entropy of each reservoir (J/K), integrated since reset
let sHot = 0;
let sCold = 0;
let t = 0;
const buf = []; // ring buffer of { t, h, c, u } samples
const BUF_MAX = 720; // ~12 s of history at 60 fps
function setup() {
createCanvas(720, 520);
pixelDensity(2);
textFont('system-ui');
textAlign(LEFT, TOP);
// sliders: always .position(x, y).size(w) -- never default-laid
thSlider = createSlider(300, 1200, 800, 1).position(40, CTRL_Y + 24).size(240);
tcSlider = createSlider(50, 299, 300, 1).position(40, CTRL_Y + 64).size(240);
qSlider = createSlider(10, 1000, 200, 1).position(340, CTRL_Y + 24).size(240);
modeBtn = createButton('mode: Carnot engine').position(340, CTRL_Y + 60).size(240, 22);
modeBtn.mousePressed(toggleMode);
resetBtn = createButton('reset stocks').position(340, CTRL_Y + 88).size(240, 22);
resetBtn.mousePressed(resetStocks);
}
function toggleMode() {
mode = (mode === 'carnot') ? 'direct' : 'carnot';
modeBtn.html(mode === 'carnot' ? 'mode: Carnot engine' : 'mode: direct conduction');
resetStocks();
}
function resetStocks() {
sHot = 0;
sCold = 0;
t = 0;
buf.length = 0;
}
function draw() {
background(BG);
// read parameters once into named locals -- physics reads as physics
let Th = thSlider.value();
let Tc = tcSlider.value();
if (Tc >= Th) Tc = Th - 1; // keep Tc strictly below Th
const Q = qSlider.value(); // heat flux drawn from hot, W
const dt = min(deltaTime / 1000, 0.05); // bounded timestep
// ---- balance equations -----------------------------------------
// Carnot: Q_h = Q, W = eta * Q, Q_c = Q - W = Q * Tc / Th
// Direct: Q_h = Q, W = 0, Q_c = Q
let eta = 0;
const Qh = Q;
let Qc = Q;
let W = 0;
if (mode === 'carnot') {
eta = 1.0 - Tc / Th;
W = eta * Q;
Qc = Q - W;
}
const dShot = -Qh / Th; // J/K per second
const dScold = Qc / Tc;
const dSuniv = dShot + dScold;
// ---- integrate (linear ODE, forward-Euler is exact-up-to-O(dt^2))
sHot += dShot * dt;
sCold += dScold * dt;
t += dt;
buf.push({ t: t, h: sHot, c: sCold, u: sHot + sCold });
if (buf.length > BUF_MAX) buf.shift();
// ---- render regions --------------------------------------------
drawReservoirs(Th, Tc, Qh, Qc, W, eta);
drawScope(SCOPE_Y, SCOPE_H);
drawControlLabels(Th, Tc, Q);
drawReadout(Th, Tc, Qh, Qc, W, eta, sHot, sCold);
drawHUD();
}
// ====================================================================
// Reservoir diagram (top region)
// Renders two tanks plus an optional Carnot engine box, with heat
// arrows whose animated tokens encode flow rate.
// ====================================================================
function drawReservoirs(Th, Tc, Qh, Qc, W, eta) {
const cy = TOP_Y + TOP_H / 2; // ~ 120
// hot reservoir on left, cold reservoir on right
drawTank(110, cy, 110, 90, HOT, 'Hot reservoir', 'T_h = ' + nf(Th, 0, 0) + ' K');
drawTank(610, cy, 110, 90, COLD, 'Cold reservoir', 'T_c = ' + nf(Tc, 0, 0) + ' K');
const arrowFromX = 110 + 55; // right edge of hot tank
const arrowToX = 610 - 55; // left edge of cold tank
if (mode === 'carnot') {
// ----- Carnot engine box in middle -------------------------
const ex = 360, ey = cy;
push();
rectMode(CENTER);
noFill(); stroke(...STRUCT); strokeWeight(2);
rect(ex, ey, 110, 78, 6);
fill(...FG); noStroke();
textAlign(CENTER, CENTER); textSize(13);
text('Carnot', ex, ey - 14);
text('engine', ex, ey + 2);
textSize(11); fill(...DIM);
text('eta = ' + nf(eta, 0, 3), ex, ey + 22);
pop();
// Q_h arrow: hot reservoir -> engine
drawHeatArrow(arrowFromX, cy, ex - 55, cy, HOT,
'Q_h = ' + nf(Qh, 0, 0) + ' W');
// Q_c arrow: engine -> cold reservoir
drawHeatArrow(ex + 55, cy, arrowToX, cy, COLD,
'Q_c = ' + nf(Qc, 0, 1) + ' W');
// W arrow upward out of engine top
drawWorkArrow(ex, ey - 40, ex, 56, 'W = ' + nf(W, 0, 1) + ' W');
} else {
// ----- direct conduction: single arrow hot -> cold ---------
drawHeatArrow(arrowFromX, cy, arrowToX, cy, HOT,
'Q = ' + nf(Qh, 0, 0) + ' W (irreversible)');
}
}
function drawTank(cx, cy, w, h, col, label, sub) {
push();
rectMode(CENTER);
// tank outline
noFill(); stroke(...col); strokeWeight(2);
rect(cx, cy, w, h, 4);
// translucent fill -- visual heat content, decorative
fill(col[0], col[1], col[2], 60); noStroke();
rect(cx, cy + 4, w - 8, h - 16, 3);
pop();
// labels above the tank
push();
textAlign(CENTER, TOP); textSize(12); fill(...FG); noStroke();
text(label, cx, cy - h / 2 - 26);
textSize(11); fill(...DIM);
text(sub, cx, cy - h / 2 - 12);
pop();
}
function drawHeatArrow(x0, y0, x1, y1, col, label) {
push();
stroke(...col); strokeWeight(3); noFill();
line(x0, y0, x1, y1);
// arrowhead
const dir = (x1 >= x0) ? 1 : -1;
fill(...col); noStroke();
triangle(x1, y1, x1 - 10 * dir, y1 - 6, x1 - 10 * dir, y1 + 6);
// moving tokens -- speed proportional to wall clock, density fixed
const len = abs(x1 - x0);
const phase = (millis() / 5) % 22;
for (let s = phase; s < len - 6; s += 22) {
const px = x0 + dir * s;
fill(255, 255, 255, 170); noStroke();
circle(px, y0, 4);
}
// label centered above the line
fill(...FG); noStroke();
textAlign(CENTER, BOTTOM); textSize(12);
text(label, (x0 + x1) / 2, y0 - 8);
pop();
}
function drawWorkArrow(x0, y0, x1, y1, label) {
push();
stroke(...GAUGE); strokeWeight(3); noFill();
line(x0, y0, x1, y1);
fill(...GAUGE); noStroke();
triangle(x1, y1, x1 - 6, y1 + 10, x1 + 6, y1 + 10);
fill(...FG); noStroke();
textAlign(LEFT, CENTER); textSize(12);
text(label, x1 + 12, (y0 + y1) / 2);
pop();
}
// ====================================================================
// Entropy scope (middle region)
// Three traces vs. time: S_hot (warm), S_cold (cool), S_univ (accent).
// Auto-scales y-axis to current data range with 10% padding.
// ====================================================================
function drawScope(y0, h) {
const x0 = 30, w = 660;
push();
noFill(); stroke(...STRUCT, 110); strokeWeight(1);
rect(x0, y0, w, h, 4);
// title
fill(...DIM); noStroke();
textAlign(LEFT, TOP); textSize(11);
text('Entropy stocks vs. time (J/K, integrated since reset)',
x0 + 8, y0 + 6);
if (buf.length < 2) {
// zero line
stroke(...SCRATCH); strokeWeight(1);
line(x0 + 6, y0 + h / 2, x0 + w - 6, y0 + h / 2);
pop();
return;
}
// find y-range across all three traces
let smin = Infinity, smax = -Infinity;
for (const s of buf) {
if (s.h < smin) smin = s.h;
if (s.c > smax) smax = s.c;
if (s.u > smax) smax = s.u;
if (s.u < smin) smin = s.u;
if (s.h > smax) smax = s.h;
if (s.c < smin) smin = s.c;
}
const pad = max(0.5, (smax - smin) * 0.1);
smin -= pad; smax += pad;
// axis labels (min/max)
fill(...DIM); noStroke();
textAlign(RIGHT, TOP); textSize(10);
text('S_max ' + nf(smax, 0, 2), x0 + w - 8, y0 + 6);
textAlign(RIGHT, BOTTOM);
text('S_min ' + nf(smin, 0, 2), x0 + w - 8, y0 + h - 6);
// zero line
const xPlotMin = x0 + 6;
const xPlotMax = x0 + w - 90; // leave room for legend at right
const tMin = buf[0].t, tMax = buf[buf.length - 1].t;
const yZero = map(0, smin, smax, y0 + h - 8, y0 + 8);
if (yZero > y0 + 4 && yZero < y0 + h - 4) {
stroke(...SCRATCH); strokeWeight(1);
line(xPlotMin, yZero, xPlotMax, yZero);
}
// closures: data -> pixel
const tx = function (tt) { return map(tt, tMin, tMax, xPlotMin, xPlotMax); };
const sy = function (ss) { return map(ss, smin, smax, y0 + h - 8, y0 + 8); };
drawTrace(buf, tx, sy, 'h', HOT);
drawTrace(buf, tx, sy, 'c', COLD);
drawTrace(buf, tx, sy, 'u', TRAJ);
// legend at right edge
const legX = x0 + w - 80, legY = y0 + 30;
drawLegend(legX, legY, HOT, 'S_hot');
drawLegend(legX, legY + 18, COLD, 'S_cold');
drawLegend(legX, legY + 36, TRAJ, 'S_univ');
// numeric current value at right of each trace
const last = buf[buf.length - 1];
textAlign(LEFT, CENTER); textSize(10); noStroke();
fill(...HOT); text(nf(last.h, 0, 2), tx(last.t) + 4, sy(last.h));
fill(...COLD); text(nf(last.c, 0, 2), tx(last.t) + 4, sy(last.c));
fill(...TRAJ); text(nf(last.u, 0, 2), tx(last.t) + 4, sy(last.u));
pop();
}
function drawTrace(samples, tx, sy, key, col) {
push();
stroke(...col); strokeWeight(2); noFill();
beginShape();
for (const s of samples) vertex(tx(s.t), sy(s[key]));
endShape();
pop();
}
function drawLegend(x, y, col, label) {
push();
noStroke(); fill(...col);
rect(x, y - 4, 12, 8, 2);
fill(...DIM); textAlign(LEFT, CENTER); textSize(11);
text(label, x + 18, y);
pop();
}
// ====================================================================
// Control labels (top of control panel region)
// ====================================================================
function drawControlLabels(Th, Tc, Q) {
push();
// outer panel border
noFill(); stroke(...STRUCT, 80); strokeWeight(1);
rect(20, CTRL_Y, 680, CTRL_H, 4);
fill(...FG); noStroke();
textAlign(LEFT, TOP); textSize(12);
text('T_hot ' + nf(Th, 0, 0) + ' K', 40, CTRL_Y + 6);
text('T_cold ' + nf(Tc, 0, 0) + ' K', 40, CTRL_Y + 46);
text('Q_in ' + nf(Q, 0, 0) + ' W (heat drawn from hot)',
340, CTRL_Y + 6);
pop();
}
// ====================================================================
// Live readout strip + canonical equations (bottom region)
// ====================================================================
function drawReadout(Th, Tc, Qh, Qc, W, eta, sH, sC) {
push();
noFill(); stroke(...STRUCT, 80); strokeWeight(1);
rect(20, READOUT_Y - 4, 680, 46, 4);
const sU = sH + sC;
const dShot = -Qh / Th;
const dScold = Qc / Tc;
const dSuniv = dShot + dScold;
fill(...FG); noStroke();
textAlign(LEFT, TOP); textSize(11);
const line1 = 'eta = 1 - Tc/Th = ' + nf(eta, 0, 3)
+ ' W = eta*Q = ' + nf(W, 0, 1) + ' W'
+ ' Q_c = ' + nf(Qc, 0, 1) + ' W';
const line2 = 'dS_h/dt = ' + nf(dShot, 0, 4)
+ ' dS_c/dt = ' + nf(dScold, 0, 4)
+ ' dS_u/dt = ' + nf(dSuniv, 0, 4) + ' (J/K/s)';
text(line1, 30, READOUT_Y + 2);
text(line2, 30, READOUT_Y + 20);
// canonical equations bottom-right (constant, identify the topic)
fill(...DIM); textAlign(RIGHT, TOP); textSize(11);
text('dS = dQ_rev / T . dS_universe >= 0',
width - 30, READOUT_Y + 2);
text('S = k_B ln W (Boltzmann)',
width - 30, READOUT_Y + 20);
pop();
}
// ====================================================================
// HUD (top-left)
// title 22pt + Wikitube subtitle 12pt + pattern tag top-right
// ====================================================================
function drawHUD() {
push();
fill(...FG); noStroke();
textAlign(LEFT, TOP); textSize(22);
text(TITLE, 14, 4);
textSize(12); fill(...DIM);
text('Wikitube microsim . en.wikitube.io/wiki/' + ARTICLE, 14, 30);
// pattern tag top-right
fill(...DIM); textAlign(RIGHT, TOP); textSize(11);
text('Helium room . Pattern K . stock-and-flow', width - 14, 8);
textAlign(RIGHT, TOP);
text('mode: ' + (mode === 'carnot' ? 'Carnot engine' : 'direct conduction'),
width - 14, 24);
pop();
}
```
## MicroSim spec
- **Recommended sim type:** stochastic process / random walk
- **Microsimmability score:** 72/100
- **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below.
### Parameters (tunable controls)
- `Number of states`
- `Probability bias`
- `Sample size`
### What animates
A probability distribution is reshaped and the entropy meter rises or falls with its spread.
### Learning objective
Relate the spread of a probability distribution to its entropy.
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Entropy.json (2026-07-30T02:09:12Z) -->
`Abdus_Salam` · `Absolute_zero` · `Absorption_refrigerator` · [[Adaptation]] · `Adiabatic_accessibility` · `Adiabatic_process` · [[Agent-based_model]] · `Airborne_wind_energy` · `Albert_Einstein` · `Amount_of_substance` · `An_Inquiry_Concerning_the_Source_of_the_Heat_Which_Is_Excited_by_Friction` · `Andreas_Albrecht_(cosmologist)` · [[Ant_colony_optimization_algorithms]] · `Anton_Zeilinger` · `Applied_physics` · `Arieh_Ben-Naim` · `Arnold_Sommerfeld` · `Arrow_of_time` · `Arthur_Compton` · [[Artificial_intelligence]] · [[Artificial_life]] · `Astrophysics` · `Atkinson_cycle` · `Atomic,_molecular,_and_optical_physics` · `Atomic_physics` · `Attenuation` · [[Attractor]] · [[Autopoiesis]] · `BBGKY_hierarchy` · `Benjamin_Thompson` · [[Bifurcation_theory]] · `Binary_logarithm` · [[Binding_energy]] · `Bioenergy` · `Biomass` · `Biophysics` · `Bit` · `Black_hole` · `Black_hole_thermodynamics` · `Boltzmann's_entropy_formula` · `Boltzmann_constant` · `Boltzmann_distribution` · `Boltzmann_equation` · `Boltzmann_machine` · [[Bounded_rationality]] · `Brady_Haran` · `Brayton_cycle` · `Bridgman's_thermodynamic_equations` · `Brownian_ratchet` · `C._V._Raman` · `Caloric_theory` · `Cambridge_University_Press` · `Canonical_ensemble` · `Capacitor` · `Carbon_footprint` · `Carnot's_theorem_(thermodynamics)` · `Carnot_cycle` · `Carnot_heat_engine` · [[Cellular_automaton]] · [[Centrality]] · `Channel_capacity` · [[Chaos_theory]] · `Charles_Coulston_Gillispie` · `Chemical_energy` · [[Chemical_engineering]] · `Chemical_equilibrium` · `Chemical_oscillator` · `Chemical_potential` · `Chemical_reaction` · `Chemical_species` · `Chemical_thermodynamics` · [[Chemistry]] · `Cheng_cycle` · `Classical_limit` · `Claude_Lévi-Strauss` · [[Claude_Shannon]] · `Clausius_theorem` · `Clifford_Truesdell` · [[Closed_system]] · `Coal` · `Cogeneration` · [[Collective_action]] · [[Collective_behavior]] · [[Collective_consciousness]] · [[Collective_intelligence]] · `Combination` · `Combined-cycle_power_plant` · [[Complex_adaptive_system]] · [[Complex_system]] · `Compressibility` · `Compressibility_factor` · `Concentrated_solar_power` · `Condensed_matter_physics` · `Configuration_entropy` · `Conformal_field_theory` · `Conformational_entropy` · `Conjugate_variables_(thermodynamics)` · `Conservation_of_energy` · `Constantin_Carathéodory` · `Control_volume` · [[Conversation_theory]] · `Correlation_function` · `Correspondence_principle` · `Cosmology` · [[Coupled_map_lattice]] · `Critical_exponent` · `Critical_phenomena` · `Cutler_J._Cleveland` · [[Cybernetics]] · `Daniel_Bernoulli` · `Dark_energy` · `David_Hilbert` · `Deformation_(physics)` · `Degenerate_energy_levels` · `Density_matrix` · `Depletion_force` · `Detailed_balance` · `Diesel_cycle` · `Dissipation` · [[Dissipative_system]] · `Drew_Dalton` · [[Dynamic_network_analysis]] · `Ecological_Economics_(journal)` · `Ecological_economics` · `Economics` · `Edward_Witten` · `Efficient_energy_use` · `Einstein_field_equations` · `Einstein_refrigerator` · `Elastic_energy` · `Electric_battery` · `Electric_potential_energy` · `Electric_power` · `Electrical_energy` · `Electricity` · `Electricity_delivery` · `Electromagnetism` · `Electroweak_interaction` · `Elementary_particle` · `Elias_Gyftopoulos` · `Elliott_H._Lieb` · `Elsevier` · [[Emergence]] · `Endoreversible_thermodynamics` · `Endothermic_process` · [[Energy]] · `Energy_carrier` · `Energy_condition` · `Energy_conservation` · `Energy_consumption` · `Energy_democracy` · `Energy_development` · `Energy_efficiency_in_agriculture` · `Energy_efficiency_in_transport` · [[Energy_engineering]] · `Energy_in_Africa` · `Energy_in_Australia` · `Energy_in_Europe` · `Energy_in_Mexico` · `Energy_in_South_America` · `Energy_in_the_United_States` · `Energy_level` · `Energy_policy` · `Energy_policy_of_Canada` · `Energy_recovery` · `Energy_recycling` · `Energy_security` · `Energy_storage` · `Energy_supply` · `Energy_system` · [[Energy_transformation]] · `Energy_transition` · `Enrico_Fermi` · `Enthalpy` · `Entropic_explosion` · `Entropic_force` · `Entropic_uncertainty` · `Entropic_value_at_risk` · `Entropy_(classical_thermodynamics)` · `Entropy_(disambiguation)` · `Entropy_(energy_dispersal)` · [[Entropy_(information_theory)]] · `Entropy_(order_and_disorder)` · `Entropy_(statistical_thermodynamics)` · `Entropy_and_life` · `Entropy_in_thermodynamics_and_information_theory` · `Entropy_of_fusion` · `Entropy_of_mixing` · `Entropy_of_vaporization` · `Entropy_production` · `Entropy_unit` · `Equation_of_state` · `Equilibrium_thermodynamics` · `Ergodic_theory` · `Ericsson_cycle` · `Ernest_Rutherford` · `Ernest_Walton` · `Erwin_Schrödinger` · `Eugene_Wigner` · `Event_horizon` · [[Evolution]] · [[Evolutionary_computation]] · [[Evolutionary_developmental_biology]] · [[Evolutionary_game_theory]] · [[Evolutionary_robotics]] · [[Evolvability]] · `Exergy` · `Exothermic_process` · [[Expected_value]] · `Experimental_physics` · [[Feedback]] · `First_law_of_thermodynamics` · `Force_field_(chemistry)` · `Fossil_fuel` · `Fossil_fuel_power_station` · [[Fractal]] · `Frank_Wilczek` · `François_Massieu` · `Frederick_Soddy` · `Free_entropy` · `Freeman_Dyson` · `Friction` · `Friedrich_Nietzsche` · `Fuel` · `Fuel_oil` · `Function_(mathematics)` · `Fundamental_thermodynamic_relation` · [[Game_theory]] · `Gas_laws` · `General_relativity` · [[Genetic_algorithm]] · [[Genetic_programming]] · [[Geomorphology]] · `Georg_Ernst_Stahl` · `George_N._Hatsopoulos` · `George_Uhlenbeck` · `Georges_Lemaître` · `Geothermal_energy` · `Geothermal_power` · `Gerard_'t_Hooft` · `Gibbs_free_energy` · `Gilbert_N._Lewis` · [[Goal_orientation]] · `Grand_canonical_ensemble` · [[Graph_theory]] · `Gravitational_binding_energy` · `Gravitational_energy` · `Gravity` · `H-theorem` · `Hamiltonian_(quantum_mechanics)` · `Hampson–Linde_cycle` · `Hawking_radiation` · `Heat` · `Heat_capacity` · `Heat_capacity_ratio` · `Heat_death_of_the_universe` · `Heat_death_paradox` · `Heat_engine` · `Heat_pump_and_refrigeration_cycle` · [[Heat_transfer]] · `Heike_Kamerlingh_Onnes` · `Helmholtz_free_energy` · `Hendrik_Lorentz` · `Henri_Becquerel` · `Henri_Poincaré` · `Henry_Moseley` · `Herbert_Callen` · [[Herd_mentality]] · `Herman_Daly` · `Hermann_Weyl` · `Hermann_von_Helmholtz` · `High-efficiency_hybrid_cycle` · `History_of_energy` · `History_of_entropy` · `History_of_perpetual_motion_machines` · `History_of_thermodynamics` · [[Homeostasis]] · `Hot_air_engine` · `Hydroelectricity` · [[Hydrogen]] · `Hydropower` · `Hygroscopic_cycle` · `Ideal_gas` · `Ideal_gas_law` · `Index_of_energy_articles` · `Inexact_differential` · `Info-metrics` · [[Information]] · [[Information_system]] · [[Information_theory]] · `Integral` · `Integrated_gasification_combined_cycle` · `Intensive_and_extensive_properties` · `Interatomic_potential` · `Internal_energy` · `Internal_pressure` · `International_System_of_Units` · `Internet_Archive` · `Introduction_to_entropy` · [[Ionization_energy]] · `Irreversible_process` · [[Isaac_Newton]] · `Isabelle_Stengers` · `Isenthalpic_process` · `Isentropic_process` · `Ising_model` · `Isobaric_process` · `Isochoric_process` · [[Isolated_system]] · `Isothermal_flow` · `Isothermal_process` · `Isothermal–isobaric_ensemble` · `J._J._Thomson` · `Jacob_Bekenstein` · `Jakob_Yngvason` · `James_Chadwick` · `James_Clerk_Maxwell` · `James_Prescott_Joule` · `Jevons_paradox` · `Johannes_Diderik_van_der_Waals` · `John_Archibald_Wheeler` · `John_Bardeen` · `John_D._Barrow` · `John_James_Waterston` · `John_Smeaton` · `John_Stewart_Bell` · [[John_von_Neumann]] · `Joseph_Henry_Keenan` · [[Josiah_Willard_Gibbs]] · `Joule` · `Journal_of_Cleaner_Production` · `Julius_von_Mayer` · `Kalina_cycle` · `Kelvin` · `Kinetic_energy` · `Kleemenko_cycle` · `Kurt_Gödel` · `Lars_Onsager` · `Latent_heat` · `Lawrence_Bragg` · `Laws_of_thermodynamics` · `Lazare_Carnot` · `Lennard-Jones_potential` · `Lenoir_cycle` · `Leon_Cooper` · `Light` · `Line_integral` · `List_of_thermodynamic_properties` · `Logarithm` · `Logarithmic_scale` · `Lord_Kelvin` · `Loschmidt's_paradox` · `Louis_de_Broglie` · `Ludwig_Boltzmann` · `M._Norton_Wise` · [[Machine_learning]] · `Magdalena_Salazar_Palma` · `Magnetic_Thermodynamic_Systems` · `Magnetic_energy` · `Marie_Curie` · `Marine_energy` · `Mass` · `Mass–energy_equivalence` · `Material_properties_(thermodynamics)` · `Mathematical_physics` · `Matter` · `Matter_wave` · `Max_Born` · `Max_Planck` · `Max_von_Laue` · `Maxwell's_demon` · `Maxwell's_thermodynamic_surface` · `Maxwell_relations` · `Mean-field_theory` · `Mechanical_energy` · `Mechanical_equivalent_of_heat` · `Mechanical_wave` · `Melting` · `Microcanonical_ensemble` · `Microstate_(statistical_mechanics)` · `Miller_cycle` · `Mixed/dual_cycle` · `Modern_physics` · `Mole_(unit)` · [[Multistability]] · `Murray_Gell-Mann` · [[Nat_(unit)]] · [[Natural_gas]] · `Natural_logarithm` · `Natural_uranium` · `Negative_energy` · `Negative_mass` · `Negentropy` · [[Network_motif]] · [[Network_science]] · [[Neural_network_(machine_learning)]] · `Neurophysics` · `Nicholas_Georgescu-Roegen` · `Nicolas_Léonard_Sadi_Carnot` · `Niels_Bohr` · `Non-equilibrium_thermodynamics` · [[Nonlinear_system]] · `Nuclear_binding_energy` · [[Nuclear_fuel]] · `Nuclear_physics` · `Nuclear_power` · `Nuclear_power_plant` · `Nucleation` · `Oil_refinery` · `On_the_Equilibrium_of_Heterogeneous_Substances` · `Onsager_reciprocal_relations` · [[Open_system_(systems_theory)]] · [[Operationalization]] · [[Ordinary_differential_equation]] · `Organic_Rankine_cycle` · `Otto_Hahn` · `Otto_Hittmair` · `Otto_cycle` · `Outline_of_energy` · [[Partial_differential_equation]] · `Particle` · `Particle_number` · `Particle_physics` · [[Particle_swarm_optimization]] · `Partition_function_(statistical_mechanics)` · `Pascual_Jordan` · [[Pattern_formation]] · `Paul_Davies` · `Paul_Dirac` · [[Percolation]] · `Percolation_theory` · `Percy_Williams_Bridgman` · `Perpetual_motion` · `Pessimism` · `Peter_Atkins` · `Peter_Higgs` · `Petroleum` · `Phase_(matter)` · [[Phase_space]] · [[Phase_transition]] · `Philipp_Lenard` · `Philipp_Mainländer` · `Philosophy_of_physics` · `Photovoltaic_system` · [[Physics]] · `Pierre_Curie` · `Pierre_Duhem` · `Pieter_Zeeman` · `Piobert's_law` · `Polytropic_process` · [[Population_dynamics]] · `Potential_energy` · `Potts_model` · `Power_(physics)` · `Power_usage_effectiveness` · `Pressure` · `Pressure_gain_combustion` · `Pressure–volume_diagram` · `Primary_energy` · `Princeton_University_Press` · `Principle_of_maximum_entropy` · [[Prisoner's_dilemma]] · [[Probability]] · `Probability_distribution` · `Process_function` · `Proportionality_(mathematics)` · `Pseudo_Stirling_cycle` · `Psychodynamics` · `Pulse_tube_refrigerator` · `Quantum_chromodynamics_binding_energy` · `Quantum_field_theory` · `Quantum_fluctuation` · `Quantum_gravity` · `Quantum_information` · [[Quantum_mechanics]] · `Quantum_potential` · `Quantum_state` · `Quantum_statistical_mechanics` · `Quantum_thermodynamics` · `Quasistatic_process` · `Quintessence_(physics)` · `Radiant_energy` · `Radiation` · `Radioisotope_thermoelectric_generator` · `Randomness` · `Rankine_cycle` · [[Rational_choice_model]] · [[Reaction–diffusion_system]] · `Real_gas` · `Reduced_properties` · `Reflections_on_the_Motive_Power_of_Fire` · `Regenerative_cooling` · `Relations_between_heat_capacities` · `Renewable_energy` · `Residual_entropy` · `Reversible_process_(thermodynamics)` · `Richard_Feynman` · `Robert_Ayres_(scientist)` · [[Robustness_(computer_science)]] · `Roger_Penrose` · `Room_temperature` · [[Rudolf_Clausius]] · `Rényi_entropy` · `SI_base_unit` · `Samuel_Goudsmit` · `Satyendra_Nath_Bose` · [[Scalability]] · [[Scale-free_network]] · `Scaling_(geometry)` · `Scholarpedia` · [[Schrödinger_equation]] · [[Science_(journal)]] · `Scuderi_cycle` · [[Second-order_cybernetics]] · [[Second_law_of_thermodynamics]] · `Self-assembly` · [[Self-organization]] · [[Self-organized_criticality]] · [[Self-reference]] · [[Self-replication]] · [[Sensemaking]] · `Sensible_heat` · `Sic` · `Siemens_cycle` · [[Small-world_network]] · [[Social_dynamics]] · [[Social_network_analysis]] · `Solar_cell` · `Solar_energy` · `Solar_furnace` · `Solar_power` · `Solar_power_tower` · `Solar_thermal_energy` · `Sound_energy` · `Space` · `Spacetime_topology` · [[Spatial_ecology]] · `Special_relativity` · `Spin_model` · `Spontaneous_process` · `Standard_molar_entropy` · `Standard_temperature_and_pressure` · `State_function` · `State_of_matter` · `State_variable` · `Statistical_field_theory` · `Statistical_mechanics` · `Statistical_model` · `Stephen_G._Brush` · `Stephen_Hawking` · `Stirling_cycle` · `Stochastic_process` · `Stoddard_engine` · `Stress_(mechanics)` · `Strong_interaction` · `Superfluidity` · `Surface_energy` · `Sustainable_energy` · [[Swarm_behaviour]] · [[Synchronization]] · `Synergetics_(Haken)` · [[System_dynamics]] · [[Systems_biology]] · [[Systems_science]] · [[Systems_theory]] · [[Systems_thinking]] · `T-symmetry` · `Table_of_thermodynamic_equations` · [[Telecommunications]] · `Temperature` · `Temperature–entropy_diagram` · `Theorem_of_corresponding_states` · `Theoretical_physics` · `Theory_of_computation` · `Theory_of_everything` · `Thermal_efficiency` · `Thermal_energy` · `Thermal_equilibrium` · `Thermal_expansion` · `Thermal_reservoir` · `Thermodynamic_cycle` · `Thermodynamic_databases_for_pure_substances` · `Thermodynamic_diagrams` · `Thermodynamic_equations` · [[Thermodynamic_equilibrium]] · `Thermodynamic_free_energy` · `Thermodynamic_instruments` · `Thermodynamic_potential` · `Thermodynamic_process` · `Thermodynamic_state` · [[Thermodynamic_system]] · `Thermodynamic_temperature` · [[Thermodynamics]] · `Thermoeconomics` · `Third_law_of_thermodynamics` · `Tidal_power` · `Time` · [[Time_series]] · `Timeline_of_heat_engine_technology` · `Timeline_of_thermodynamics` · `Trace_class` · `Transcritical_cycle` · `Tsallis_entropy` · `Tsung-Dao_Lee` · `Units_of_energy` · `University_of_Nottingham` · `Vacuum_energy` · `Vapor_quality` · [[Variety_(cybernetics)]] · `Vis_viva` · [[Viscosity]] · `Vlasov_equation` · `Volume_(thermodynamics)` · `Volumetric_flow_rate` · `Von_Neumann_entropy` · `Vuilleumier_cycle` · `Walther_Nernst` · `Waste-to-energy` · `Waste-to-energy_plant` · `Water_wheel` · [[Wave]] · `Wave_function_collapse` · [[Wayback_Machine]] · `Weak_interaction` · `Werner_Heisenberg` · `Wilhelm_Röntgen` · `Wilhelm_Wien` · `William_Shockley` · `Wind_farm` · `Wind_power` · `Wolfgang_Pauli` · `Work_(physics)` · `Work_(thermodynamics)` · `World_energy_supply_and_consumption` · `Yang_Chen-Ning` · `Yoichiro_Nambu` · [[Zero-point_energy]] · `Zeroth_law_of_thermodynamics`
<!-- GIFPLATE:BEGIN v1.0 g16 — Commons hotlink; do not hand-edit inside -->
## Images
<figure class="wt-gifplate">
<img src="https://commons.wikimedia.org/wiki/Special:FilePath/Neural_Network.gif" alt="Neural Propagation" loading="lazy" decoding="async">
<figcaption><strong>Neural Propagation</strong> — Illustrate information propagation through layered networks.<br>
<span class="wt-credit">Wikimedia Commons · <strong>licence pending verification</strong> (run <code>g17_gif_verify.py</code> on a networked lane) · <a href="https://commons.wikimedia.org/wiki/File:Neural_Network.gif">Details</a></span></figcaption>
</figure>
*Still companion to the 1 live microsim above: the sim is the instrument, the plate is the glance. §15 keeps the player first; this sits in the image slot on [[Entropy]].*
<!-- GIFPLATE:END -->
## From the Real GENERATIVE library (beauty pass)
*Entropy — image hotlinked from Wikimedia Commons (via the Real G.E.N.E.R.A.T.I.V.E. course library, Energy room). [Details & license](https://commons.wikimedia.org/wiki/File:Carnot_heat_engine_2.svg).*
> Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour ([Wikipedia](https://en.wikipedia.org/wiki/Entropy))
<!-- BEAUTY-PASS-MEDIA:END -->
> **Room:** [[Helium]] · **Status:** ✅ shipped
## Overview
Entropy is a state function in [[Thermodynamics|thermodynamics]] quantifying the unavailability of a [[System|system]]'s [[Energy|energy]] for conversion into mechanical work, equivalently a measure of microscopic disorder or the number of accessible microstates. [[Rudolf_Clausius|Rudolf Clausius]] introduced it in 1865 with the definition dS = dQ_rev / T, where dQ_rev is reversible [[Heat_transfer|heat transfer]] at absolute temperature T; the symbol S and the term "entropy" (Greek tropi, transformation) are his. The [[Second_law_of_thermodynamics|Second Law of Thermodynamics]] states that the entropy of an [[Isolated_system|isolated system]] never decreases: dS_universe >= 0, identifying the arrow of time. Ludwig Boltzmann gave entropy a statistical foundation in 1877, S = k_B ln W, where k_B is Boltzmann's constant and W is the multiplicity of microstates consistent with a macrostate; [[Josiah_Willard_Gibbs|Josiah Willard Gibbs]] generalized this to S = -k_B sum p_i ln p_i for a probability distribution over microstates. The Third Law of Thermodynamics (Nernst, 1906) sets the entropy of a perfect crystal to zero at T = 0 K. Entropy is central to chemical thermodynamics through the Gibbs free energy G = H - TS, governing reaction spontaneity, and to [[Cryogenics|cryogenics]] through adiabatic-demagnetization and Joule-Thomson cooling cycles that exploit the temperature dependence of S(T, P). [[Claude_Shannon|Claude Shannon]] extended the formalism to [[Information_theory|information theory]] in 1948 as H = -sum p_i log2 p_i, the foundation of modern coding and cryptography. Black-hole thermodynamics (Bekenstein-Hawking, S = k_B A / 4 L_P^2) shows the concept extends to gravitation.
## See also
- Room hub: [[Helium]]
- p5.js Editor conventions: P5 JS EDITOR
- Wiki root: MAIN
---
*Scaffolded by `generative-microsim` from row 117 of the Helium sheet on 2026-05-14T12:25:54Z.*
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<!-- CRAFT-LINK:START g12 -->
*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Entropy) : [Wikitube](https://en.wikitube.io/wiki/Entropy)
## Previous hub tags
Tree parents: [[Complex_system]] · [[Cybernetics]] · [[Emergence]] · [[Feedback]] · [[Self-organization]] · [[Systems_science]] · [[Systems_theory]].
Legacy hubs: none.
---
*Sources: 2 legacy notes. Minted wave 1, 2026-07-30 (v1.6 order).*