Editing Thermodynamics (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Simulating a 2D Ising Model (Ferromagnetism):'''
<syntaxhighlight lang="python">
import numpy as np

def ising_step(lattice, beta, J=1.0):
    """Perform one Metropolis-Hastings step for the Ising model."""
    N = lattice.shape[0]
    for _ in range(N*N):
        i, j = np.random.randint(0, N, 2)
        # Sum of neighbors (periodic boundary conditions)
        neighbors = lattice[(i+1)%N, j] + lattice[(i-1)%N, j] + \
                    lattice[i, (j+1)%N] + lattice[i, (j-1)%N]
        
        # Change in energy if we flip this spin
        delta_E = 2 * J * lattice[i, j] * neighbors
        
        # Accept flip if energy decreases or with probability exp(-beta*dE)
        if delta_E <= 0 or np.random.rand() < np.exp(-beta * delta_E):
            lattice[i, j] *= -1
    return lattice

# Setup 20x20 lattice
lattice = np.random.choice([1, -1], size=(20, 20))
temp = 2.0
beta = 1.0 / temp

# Run for 1000 steps
for _ in range(1000):
    lattice = ising_step(lattice, beta)

print("Final Average Magnetization:", np.mean(lattice))
</syntaxhighlight>

; Practical Applications
: '''Engine Design''' — Carnot cycle limits, fuel efficiency, turbochargers.
: '''Materials Science''' — Predicting alloys, melting points, superconductivity transitions.
: '''Meteorology''' — Atmospheric pressure, convection, hurricane formation.
: '''Chemistry''' — Chemical equilibrium, protein folding, reaction rates.
: '''Information Theory''' — Shannon entropy, data compression (mathematical cousin of physical entropy).
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