Modern Thermodynamics with Julia in CoCalc

import Pkg; Pkg.add("PlotThemes")

using Plots, Printf, Statistics, LinearAlgebra
using PlotThemes
theme(:bright)

# Physical constants (SI)
const k_B = 1.380649e-23       # Boltzmann constant (J/K)
const h   = 6.62607015e-34     # Planck constant (J·s)

println("⚛️ MODERN THERMODYNAMICS: QUANTUM & NANOSCALE")
println(repeat("=", 55))
println("Exploring thermodynamics at quantum and molecular scales")
println()
println("Quantum Constants:")
println("• Boltzmann constant: k_B = $(k_B) J/K")
println("• Planck constant: h = $(h) J·s")

using Printf

# Physical constants (SI)
const k_B = 1.380649e-23       # Boltzmann constant (J/K)
const h   = 6.62607015e-34     # Planck constant (J·s)

println("=== QUANTUM AND NANOSCALE THERMODYNAMICS ===")

# Landauer's principle
function landauer_energy(T)
    # minimum energy to erase one bit
    return k_B * T * log(2)
end

# Thermal de Broglie wavelength: λ = h/√(2π m k_B T)
function thermal_de_broglie(T, mass)
    return h / sqrt(2π * mass * k_B * T)
end

# Einstein relation: D = k_B T / (6π η r) for spherical particle
function diffusion_coefficient(T, radius, viscosity)
    return k_B * T / (6π * viscosity * radius)
end

println("=== INFORMATION THERMODYNAMICS ===")
println("Landauer's Principle: Energy Cost of Information Processing")
println()

temperatures = [4, 77, 300, 373]  # K (liquid helium, liquid N₂, room temp, boiling water)
temp_names = ["Liquid He", "Liquid N₂", "Room temp", "Boiling H₂O"]

println("Minimum Energy to Erase One Bit (Landauer Limit):")
println(repeat("-", 60))
@printf "%-15s %8s %15s %15s\n" "Temperature" "T (K)" "Energy (J)" "Energy (eV)"
println(repeat("-", 60))

for (i, T) in enumerate(temperatures)
    E_landauer = landauer_energy(T)
    E_eV = E_landauer / 1.602176634e-19  # Convert to eV
    @printf "%-15s %8.0f %15.2e %15.2e\n" temp_names[i] T E_landauer E_eV
end

println()
println("Information Processing Insights:")
println("• Colder computers are more energy-efficient")
println("• Quantum computers cooled to millikelvin temperatures")
println("• Modern processors dissipate ~10⁶ times Landauer limit")
println("• Room for dramatic improvement in reversible computing")
println()

# Quantum vs classical regimes
println("=== QUANTUM VS CLASSICAL REGIMES ===")
println("Thermal de Broglie Wavelength")
println()

particles = [
    ("Electron", 9.109e-31),
    ("Proton", 1.673e-27),
    ("H₂ molecule", 3.3e-27),
    ("Virus (100 nm)", 1e-15),
    ("Dust (1 μm)", 1e-12)
]

T_room = 300  # K

println("Thermal de Broglie wavelengths at T = $T_room K:")
println(repeat("-", 70))
@printf "%-15s %12s %15s %15s\n" "Particle" "Mass (kg)" "λ_thermal (m)" "Quantum?"
println(repeat("-", 70))

for (particle, mass) in particles
    λ_th = thermal_de_broglie(T_room, mass)
    quantum_regime = λ_th > 1e-10 ? "Yes" : "No"  # Rough criterion
    @printf "%-15s %12.2e %15.2e %15s\n" particle mass λ_th quantum_regime
end

println()
println("Quantum Regime Criteria:")
println("• Thermal wavelength comparable to system size")
println("• Light particles more likely to show quantum effects")
println("• Lower temperatures enhance quantum behavior")
println("• Macroscopic objects are classical")
println()

# Nanoscale Brownian motion
println("=== NANOSCALE BROWNIAN MOTION ===")
η_water = 1e-3  # Pa⋅s (water viscosity)
T_body = 310    # K (body temperature)

nano_objects = [
    ("Small molecule", 1e-9),
    ("Protein", 5e-9),
    ("Virus", 50e-9),
    ("Bacterium", 1e-6),
    ("Cell", 10e-6)
]

println("Diffusion in Water at Body Temperature:")
println(repeat("-", 70))
@printf "%-15s %12s %15s %15s\n" "Object" "Radius (m)" "D (m²/s)" "Distance/s (μm)"
println(repeat("-", 70))

for (object, radius) in nano_objects
    D = diffusion_coefficient(T_body, radius, η_water)
    distance_per_sec = sqrt(2 * D * 1) * 1e6  # RMS distance in 1 second, in μm
    @printf "%-15s %12.2e %15.2e %15.1f\n" object radius D distance_per_sec
end

println()
println("Nanoscale Transport Insights:")
println("• Smaller objects diffuse faster")
println("• Thermal motion dominates at nanoscale")
println("• Molecular motors work against Brownian motion")
println("• Diffusion-limited reaction rates")
println("• No Reynolds number effects (Stokes flow)")
println()