Power-Law Collapse: Structure, Entropy, and the Ultimate Equation of Complexity baixar o livro de graça

The Second Law of Thermodynamics says entropy never decreases.

That is correct — but incomplete.

It tells us the universe ends in heat death, but not why it assembles stars, cells, minds, and civilizations along the way. It gives us a direction, but no speed — and no acceleration.

Acceleration is the heart of the problem.

Starting from Kleiber's Law and the WBE fractal network theory, this book derives a single equation governing the growth and collapse of complexity across every known scale:

dC/dt = α·Cγ − κ·Cδ (δ > γ)

The growth term α·Cγ captures the power-law return on energy input. The maintenance term κ·Cδ captures the super-power-law cost of connections. When the maintenance exponent δ exceeds the growth exponent γ — and it does in every known complex system — collapse is not an accident. It is a mathematical inevitability.

• The 3/4-power tyranny — why metabolic rate scales as body mass to the 3/4 and what this means for every living system
• From cells to cities — how organisms, cities, and corporations obey the same scaling laws
• The entropy ledger — maintenance, information, and growth costs; Landauer's principle; Earth as a visible entropy engine
• Borrowed order — dissipative structures, low-entropy capital, and why every system eventually "repays the loan"
• Stellar borrowing — the star's onion-shell structure, silicon-to-iron in under a day, and three modes of collapse
• Earth's coevolution — from 12 primordial minerals to 5,800 species, the Boring Billion, and seven planetary state transitions
• The peak of consciousness — the human brain as the densest known complexity structure in the universe, and its thermodynamic price

Are fascinated by complexity, thermodynamics, and cosmology. This book does not shy from equations, but always leads with physical intuition. It is precise, unsentimental, and offers no comfort.

Yunyi Yan (Stanley Yan) a multidisciplinary researcher with extensive expertise in complexity science and artificial intelligence. With years of deep engagement in these cutting-edge fields, Yan combines broad scholarly knowledge with a passion for exploring the frontiers of science and technology. An avid traveler and seasoned backpacker, Yan has journeyed through dozens of countries, embracing diverse cultures and perspectives that enrich both his personal and academic insights. His work reflects a rare blend of rigorous analysis and global curiosity, making him a distinctive voice in contemporary research.

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