---
id: wiki-2026-0508-dissipative-structures
title: Dissipative Structures
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Far-from-Equilibrium Systems, Self-Organization, Prigogine Systems]
duplicate_of: none
source_trust_level: A
confidence_score: 0.88
verification_status: applied
tags: [thermodynamics, self-organization, complexity, nonlinear-dynamics, prigogine]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: numpy/scipy
---

# Dissipative Structures

## 매 한 줄
> **"매 open systems far from equilibrium, fed energy/matter, spontaneously self-organize into ordered patterns by exporting entropy"**. 매 1977 Ilya Prigogine Nobel — 매 Bénard convection cells, BZ chemical oscillations, hurricanes 부터 매 living cells, neural avalanches, economy, 매 LLM 의 emergent capabilities 까지 매 explanatory framework.

## 매 핵심

### 매 핵심 조건
1. **Open system**: 매 energy/matter exchange with environment.
2. **Far from equilibrium**: 매 driven by external gradient (heat, chemical potential).
3. **Nonlinearity**: 매 positive feedback / autocatalysis.
4. **Entropy export**: 매 dS_system < 0 가능 — 매 dS_universe > 0 유지하며.

### 매 mathematical core
- **Entropy production**: `σ = dS/dt = Σ J_i · X_i` (fluxes × forces).
- **Bifurcation**: 매 control parameter μ 변화 시 매 stable state branch 점프.
- **Order parameter**: 매 emergent macroscopic variable (Haken synergetics).
- **Dissipation theorem**: 매 stable structure must produce entropy.

### 매 examples (low → high complexity)
- **Bénard cells**: 매 fluid heated below → hexagonal convection.
- **BZ reaction**: 매 chemical concentration spiral waves.
- **Laser**: 매 above pumping threshold, photons coherent.
- **Hurricane**: 매 ocean heat → organized vortex.
- **Cell**: 매 metabolism = continuous dissipation.
- **Ecosystem / Economy**: 매 energy throughput → structure.

### 매 응용
1. **AI training**: 매 SGD as far-from-equilibrium dynamics, loss landscape exploration.
2. **Neural avalanches**: 매 brain at criticality, 매 neuronal cascades self-organize.
3. **Self-organizing networks**: 매 ant colony, swarm robotics.
4. **Active matter**: 매 collective motion of self-propelled particles.

## 💻 패턴

### Lorenz System (Classic Dissipative Chaos)
```python
import numpy as np
from scipy.integrate import odeint

def lorenz(state, t, sigma=10, rho=28, beta=8/3):
    x, y, z = state
    return [sigma*(y-x), x*(rho-z)-y, x*y - beta*z]

t = np.linspace(0, 40, 10000)
sol = odeint(lorenz, [1,1,1], t)
# Strange attractor — entropy produced as trajectory dissipates onto fractal set
```

### Bénard Convection (Rayleigh-Bénard simplified)
```python
def rayleigh_benard_2d(T_top, T_bot, viscosity, k_thermal, dt, T_grid):
    """Boussinesq + buoyancy → convection cells appear above critical Rayleigh number."""
    Ra = (T_bot - T_top) * gravity * thermal_expansion / (viscosity * k_thermal)
    if Ra > 1708:  # critical
        # initiate convection rolls
        ...
    # iterate Navier-Stokes + heat eq with periodic BC
```

### BZ Reaction (Oregonator)
```python
def oregonator(state, t, eps=0.04, q=8e-4, f=1):
    x, y, z = state
    dx = (x*(1-x) - f*z*(x-q)/(x+q)) / eps
    dy = x - y
    dz = x - z
    return [dx, dy, dz]
```

### Detecting Self-Organization (Order Parameter)
```python
def order_parameter_kuramoto(phases):
    """|<e^{iθ}>| — Kuramoto sync order param. 1=fully synced, 0=incoherent."""
    return np.abs(np.mean(np.exp(1j * phases)))

# Sweep coupling K → bifurcation at K_c
for K in np.linspace(0, 5, 50):
    phases = simulate_kuramoto(N=500, K=K, T=200)
    print(K, order_parameter_kuramoto(phases))
```

### Edge-of-Chaos Detector (Lyapunov)
```python
def max_lyapunov(traj_fn, x0, dt=0.01, T=1000, eps=1e-9):
    x, x_pert = x0.copy(), x0 + eps
    sum_log = 0; n = 0
    for _ in range(int(T/dt)):
        x = traj_fn(x, dt); x_pert = traj_fn(x_pert, dt)
        d = np.linalg.norm(x_pert - x)
        sum_log += np.log(d / eps); n += 1
        x_pert = x + (x_pert - x) * eps / d  # rescale
    return sum_log / (n * dt)
# λ > 0: chaos; λ ≈ 0: edge-of-chaos (rich self-organization)
```

### Maximum Entropy Production Principle (MEP)
```python
def select_steady_state(states, entropy_production_fn):
    """Among possible steady states, system selects one maximizing dS/dt."""
    return max(states, key=entropy_production_fn)
```

## 매 결정 기준
| 상황 | Framework |
|---|---|
| Pattern formation in fluids | Rayleigh-Bénard, reaction-diffusion |
| Coupled oscillators sync | Kuramoto |
| Chemical autocatalysis | Brusselator / Oregonator |
| Brain criticality | neural avalanche, Hopfield |
| Open economic systems | non-equilibrium econophysics |
| ML loss landscapes | SGD as Langevin, basin escape |

**기본값**: 매 모델링 시 매 forcing (energy input) + nonlinear feedback + dissipation 매 명시적 표현.

## 🔗 Graph
- 부모: [[Thermodynamics]] · [[Nonlinear-Dynamics]] · [[Complexity Science]]
- 응용: [[Emergence-in-Systems]]
- Adjacent: [[Entropy in Information Theory]] · [[Chaos-Theory in Systems]] · [[Free-Energy-Principle]]

## 🤖 LLM 활용
**언제**: 매 emergent capability 의 thermodynamic interpretation, 매 generative model 의 entropy budget analysis.
**언제 X**: 매 simple equilibrium statistical mechanics — 매 dissipative framework 가 overhead.

## ❌ 안티패턴
- **2nd law violation 주장**: 매 local order 가 global entropy increase 를 보상한다는 점 누락.
- **Equilibrium thermodynamics 적용**: 매 living systems 는 매 inherently far-from-equilibrium.
- **Reductionism**: 매 microscopic dynamics 만으로 매 macro pattern 설명 불가 — 매 emergent order parameter 필요.

## 🧪 검증 / 중복
- Verified (Prigogine 1977 Nobel lecture; Nicolis & Prigogine 1989 *Exploring Complexity*; Haken 1983 *Synergetics*).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — full content with Lorenz, BZ, Kuramoto, Lyapunov |
