---
slug: convergence-encyclopedia-part-2-schools-physical
title: Convergence Encyclopedia: The Schools — Physical & Formal Sciences
canonical: https://miscsubjects.com/a/convergence-encyclopedia-part-2-schools-physical
---

## PART 2: THE SCHOOLS — PHYSICAL & FORMAL SCIENCES

## 2.1 Physics & Cosmology

Classical Mechanics

•	Founder(s): Isaac Newton (Philosophiæ Naturalis Principia Mathematica, 1687); Joseph-Louis Lagrange (Mécanique Analytique, 1788); William Rowan Hamilton (Hamilton’s equations, 1833)
•	Core claim: Bodies follow paths determined by extremal principles — least action governs motion
•	Convergence patterns: C02 (least action), C03 (symmetry-conservation via Noether’s later theorem applied to Lagrangians), C07 (Hamiltonian dynamics as homeostatic flow on phase space)
•	Independence check: Derived from celestial mechanics and billiard-ball collisions — independent of thermodynamics or biology by >150 years
•	Claim tier: T0 — empirically confirmed to 10^-17 precision (LIGO, lunar ranging)
•	Key tension: Hamiltonian mechanics is time-reversible; contradicts C01 (gradient dissipation) which is irreversible. The arrow-of-time problem remains open
•	Canonical text: Landau & Lifshitz, Mechanics (1960), Ch. 1-2 on least action

Electromagnetism

•	Founder(s): James Clerk Maxwell (A Treatise on Electricity and Magnetism, 1873); consolidated by Heaviside into four equations
•	Core claim: Electric and magnetic fields are one unified field whose dynamics are governed by charge conservation and Lorentz invariance
•	Convergence patterns: C02 (Maxwell’s equations derive from least action), C03 (gauge symmetry → charge conservation, Noether), C14 (wave-particle duality of electromagnetic radiation), C18 (waves as fundamental excitation)
•	Independence check: Independent — emerged from experimental work on static electricity, magnetism, and optics, not from mechanics or thermodynamics
•	Claim tier: T0 — quantum electrodynamics most precisely confirmed theory in physics (g-2 to 10^-10)
•	Key tension: Maxwell’s equations are time-symmetric (microscopic reversibility); contradicts the macroscopic irreversibility of C01 and thermodynamics
•	Canonical text: Jackson, Classical Electrodynamics (3rd ed., 1999), Ch. 11 on gauge invariance

Thermodynamics

•	Founder(s): Sadi Carnot (Réflexions sur la Puissance Motrice du Feu, 1824); Rudolf Clausius (entropy, 1865); Ludwig Boltzmann (S = k log W, 1877); J. Willard Gibbs (On the Equilibrium of Heterogeneous Substances, 1876)
•	Core claim: Energy is conserved; entropy of isolated systems increases monotonically to a maximum
•	Convergence patterns: C01 (gradient dissipation — heat flows down temperature gradients), C06 (entropy as information/missing knowledge), C07 (equilibrium as homeostasis)
•	Independence check: Independent — Carnot was an engineer studying steam engines, not doing fundamental physics. Clausius synthesized from heat-engine experiments
•	Claim tier: T0 — no violations of 1st/2nd law ever observed
•	Key tension: Boltzmann’s probabilistic interpretation of entropy vs. Gibbs’ ensemble view creates tension with quantum measurement. Also: Loschmidt’s paradox — time-symmetric microdynamics vs. time-asymmetric macro-entropy
•	Canonical text: Gibbs, Elementary Principles in Statistical Mechanics (1902), Ch. 1-4 on ensemble theory

Special & General Relativity

•	Founder(s): Albert Einstein (“On the Electrodynamics of Moving Bodies,” 1905; “The Field Equations of Gravitation,” 1915); contributions from Lorentz, Poincaré, Minkowski, Hilbert
•	Core claim: Spacetime is a dynamical geometry; the speed of light is invariant; gravity is curvature
•	Convergence patterns: C02 (Einstein-Hilbert action is a least-action principle), C03 (general covariance → energy-momentum conservation), C10 (scale invariance in certain limits), C14 (duality between mass and energy, E=mc²)
•	Independence check: Independent — Einstein was a patent clerk reasoning about light signals, not building on thermodynamics or biology
•	Claim tier: T0 — GPS corrections require GR daily; black hole imaging confirms predictions
•	Key tension: GR is deterministic and local; QM is probabilistic and nonlocal. Their marriage remains the central unsolved problem
•	Canonical text: Einstein, “The Foundation of the General Theory of Relativity” (1916), Annalen der Physik, Vol. 49

Quantum Mechanics

•	Founder(s): Max Planck (quantization of radiation, 1900); Werner Heisenberg (matrix mechanics, 1925); Erwin Schrödinger (wave equation, 1926); Paul Dirac (bra-ket formalism, relativistic equation, 1928); Richard Feynman (path integral, 1948)
•	Core claim: Physical quantities are quantized; measurement outcomes are probabilistic; the universe is described by unitary evolution of wavefunctions in Hilbert space
•	Convergence patterns: C02 (Feynman path integral = sum over all histories, a global extremal principle), C03 (symmetries → conserved quantities, Noether theorem in QM), C05 (quantum criticality), C06 (von Neumann entropy as information), C14 (wave-particle complementarity), C18 (Schrödinger equation as wave equation)
•	Independence check: Independent — Planck solved blackbody radiation; Heisenberg built from atomic spectra; Schrödinger from de Broglie matter-waves. Different starting points, same mathematical structure
•	Claim tier: T0 — Bell inequality violations, quantum computing, spectroscopy all confirm
•	Key tension: Measurement problem — unitary evolution (Schrödinger) vs. wavefunction collapse (Born rule). QM and GR are formally incompatible at singularities
•	Canonical text: Dirac, The Principles of Quantum Mechanics (1930), Ch. 1-3 on superposition and observables

Quantum Field Theory & Standard Model

•	Founder(s): Dirac, Feynman, Schwinger, Tomonaga (QED, 1940s); Yang & Mills (gauge theory, 1954); Glashow-Weinberg-Salam (electroweak, 1961-67); Gell-Mann (QCD, 1964); Higgs mechanism (1964); confirmed by LHC (2012)
•	Core claim: All particles are excitations of quantum fields; forces are mediated by gauge bosons; symmetries constrain all interactions
•	Convergence patterns: C02 (action principle), C03 (gauge symmetry → force carriers; Noether charges), C04 (spontaneous symmetry breaking → Higgs mechanism → mass), C06 (entanglement entropy), C14 (wave-particle, matter-antimatter dualities)
•	Independence check: Built on QM + special relativity, not on biology or economics. Independent tradition
•	Claim tier: T0 — Higgs boson detected; g-2 calculated to 10 digits; all predictions confirmed
•	Key tension: Standard Model cannot explain dark matter, dark energy, neutrino masses, or gravity. Needs beyond-SM physics
•	Canonical text: Peskin & Schroeder, An Introduction to Quantum Field Theory (1995), Ch. 2-4 on canonical quantization and path integrals

Cosmology & the Arrow of Time

•	Founder(s): Albert Einstein (cosmological model, 1917); Georges Lemaître (Big Bang, 1927); Edwin Hubble (expansion, 1929); Roger Penrose (Weyl curvature hypothesis, 1979); Alan Guth (inflation, 1980)
•	Core claim: The universe began in a low-entropy hot dense state and has been expanding and cooling ever since
•	Convergence patterns: C01 (entropy increase drives cosmic evolution), C04 (symmetry-breaking: hot early universe had unified forces, broke as it cooled), C05 (inflation ends at criticality), C06 (cosmic information content grows), C24 (fine-tuning of constants), C25 (teleology of cosmic evolution — contested)
•	Independence check: Emerged from applying GR to the universe + thermodynamics, independent of biology or computation
•	Claim tier: T1 — Big Bang confirmed by CMB, nucleosynthesis, expansion; but inflation, multiverse, and arrow-of-time explanations remain speculative
•	Key tension: Boltzmann brain problem: if entropy fluctuates, ordered brains are more likely than whole ordered universes. Penrose’s Weyl curvature hypothesis attempts resolution but is unproven
•	Canonical text: Penrose, The Road to Reality (2004), Ch. 27-28 on the arrow of time

Non-Equilibrium Thermodynamics

•	Founder(s): Lars Onsager (reciprocal relations, 1931); Ilya Prigogine (dissipative structures, Introduction to Thermodynamics of Irreversible Processes, 1955; Nobel 1977); Gregoire Nicolis & Isabelle Stengers (Order Out of Chaos, 1984)
•	Core claim: Systems far from equilibrium can spontaneously organize into ordered structures maintained by energy/matter flows
•	Convergence patterns: C01 (gradient dissipation drives the process), C05 (self-organization at criticality/edge of chaos), C07 (feedback maintains structure), C12 (self-maintaining structures as proto-life)
•	Independence check: Independent — Prigogine started from chemical kinetics and thermodynamics, not biology or computation. Converged with biology later
•	Claim tier: T2 — Bénard convection and Belousov-Zhabotinsky reactions confirm the phenomenon; claims about life and complexity as dissipative structures are more speculative
•	Key tension: Prigogine claimed thermodynamics explains the arrow of time; this contradicts the gravitational/statistical mechanics explanations and remains disputed
•	Canonical text: Prigogine & Stengers, Order Out of Chaos (1984), Part III on dissipative structures

## 2.2 Mathematics

Calculus & Analysis

•	Founder(s): Isaac Newton (Method of Fluxions, 1671); Gottfried Leibniz (Nova Methodus, 1684); Augustin-Louis Cauchy (rigorous limits, 1821); Karl Weierstrass (ε-δ definition, 1861)
•	Core claim: Continuous change can be captured by limits of ratios and sums, enabling the study of rates and accumulations
•	Convergence patterns: C02 (calculus is the tool of least-action physics), C08 (self-reference in differential equations that describe their own solutions), C10 (analysis of fractal limits)
•	Independence check: Independent — Newton solved mechanics problems; Leibniz sought a universal characteristic. Both invented calculus independently
•	Claim tier: T0 — foundational; all physics and engineering depend on it
•	Key tension: The foundations crisis (19th c.) — infinitesimals vs. limits — mirrors the tension between discrete and continuous in C20 (computation)
•	Canonical text: Courant & John, Introduction to Calculus and Analysis (1965), Vol. 1, Ch. 1-3 on limits and continuity

Calculus of Variations

•	Founder(s): Leonhard Euler (Methodus Inveniendi, 1744); Joseph-Louis Lagrange (Euler-Lagrange equation, 1755); William Rowan Hamilton (Hamilton’s principle, 1834); Carl Jacobi (conjugate points, 1837)
•	Core claim: The path taken by a system between two states extremizes an action functional — nature optimizes
•	Convergence patterns: C02 (least action — the defining principle), C15 (optimization over function spaces), C16 (optimal paths as geodesics), C17 (catenary curves, brachistochrone as optimal curves)
•	Independence check: Independent — Euler and Lagrange were solving mathematical problems (shortest curves, fastest descent), not doing physics. The physical interpretation came later
•	Claim tier: T0 — least action is the foundation of all modern physics
•	Key tension: Variational principles are teleological (C25) — the system “knows” the endpoint. This bothered Mauperturis and continues to raise foundational questions
•	Canonical text: Gelfand & Fomin, Calculus of Variations (1963), Ch. 1-3 on the Euler-Lagrange equation

Group Theory & Symmetry

•	Founder(s): Évariste Galois (permutation groups, 1830); Sophus Lie (continuous transformation groups, 1874); Emmy Noether (Noether’s theorem, 1918); Eugene Wigner (group theory in QM, 1931)
•	Core claim: Mathematical structure is organized by symmetry operations; every continuous symmetry of a physical system implies a conservation law
•	Convergence patterns: C02 (symmetries constrain the action), C03 (symmetry ↔ conservation — Noether’s theorem is this pattern’s formal expression), C04 (symmetry-breaking reveals structure), C10 (symmetry groups have invariant substructures at all scales)
•	Independence check: Independent — Galois solved polynomial equations; Lie studied differential equations; Noether unified them. Pure mathematics, later applied to physics
•	Claim tier: T0 — Noether’s theorem is a theorem; its physical application is confirmed daily in particle physics
•	Key tension: The “unreasonable effectiveness” of mathematics (Wigner, 1960) — why should symmetry groups describe nature at all? Unresolved
•	Canonical text: Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (1959), Ch. 1 on symmetry principles

Topology

•	Founder(s): Henri Poincaré (Analysis Situs, 1895; Poincaré conjecture, 1904)
•	Core claim: Properties of spaces are preserved under continuous deformation; global structure constrains local dynamics
•	Convergence patterns: C03 (topological invariants as conserved quantities), C10 (scale invariance — topology ignores metric/scale), C23 (attractors have topological structure)
•	Independence check: Independent — Poincaré invented topology to study celestial mechanics (three-body problem), a completely different motivation from algebra or analysis
•	Claim tier: T0 — Poincaré conjecture proven by Perelman (2003); topological quantum field theories (Witten) are active research
•	Key tension: Topology is qualitative and continuous; computation is discrete. Their intersection (computational topology) is recent and contested
•	Canonical text: Poincaré, Analysis Situs (1895), translated in Papers on Topology (AMS, 2010), opening sections

Information Theory

•	Founder(s): Claude Shannon (“A Mathematical Theory of Communication,” 1948); Andrey Kolmogorov (algorithmic complexity, 1965); Ray Solomonoff (universal prior, 1964); Gregory Chaitin (Ω, halting probability, 1975)
•	Core claim: Information can be quantified in bits; the information content of an object is the length of the shortest program that generates it
•	Convergence patterns: C06 (entropy = Shannon information = missing information), C08 (self-reference in Chaitin’s Ω), C20 (universal computation — Turing machines as the framework for algorithmic information), C09 (compression as selection of efficient codes)
•	Independence check: Shannon was at Bell Labs solving communication engineering problems. Independent of physics or biology. Kolmogorov was a pure mathematician
•	Claim tier: T0 — Shannon’s coding theorems are mathematical theorems; Kolmogorov complexity is well-defined. Applications are T1-T2
•	Key tension: Kolmogorov complexity is uncomputable (no algorithm can compute K(x) for all x). This is a fundamental limit, not a practical one
•	Canonical text: Shannon & Weaver, The Mathematical Theory of Communication (1949), Ch. 1 on the discrete noiseless channel

Logic & Computability

•	Founder(s): Gottlob Frege (Begriffsschrift, 1879); Bertrand Russell & Alfred Whitehead (Principia Mathematica, 1910-13); Kurt Gödel (incompleteness theorems, 1931); Alan Turing (Turing machine, 1936; halting problem); Alonzo Church (λ-calculus, 1936)
•	Core claim: There are well-defined limits to what can be computed or proved; formal systems are either incomplete or inconsistent
•	Convergence patterns: C08 (self-reference — Gödel’s proof uses self-referential statements), C20 (universal computation — Turing-complete systems), C06 (information as the measure of computational complexity)
•	Independence check: Independent — Frege wanted to reduce mathematics to logic; Gödel responded to Hilbert’s program; Turing solved the Entscheidungsproblem. Pure mathematics, no empirical motivation
•	Claim tier: T0 — Gödel’s theorems are proved theorems; Church-Turing thesis is widely accepted
•	Key tension: Church-Turing thesis limits physical computation, but quantum computing may (or may not) violate it. The Extended Church-Turing thesis is actively contested
•	Canonical text: Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem” (1936), Proceedings of the London Mathematical Society, §1-4 on computable numbers

Dynamical Systems

•	Founder(s): Henri Poincaré (qualitative theory of differential equations, 1890s); Aleksandr Lyapunov (stability theory, 1892); Edward Lorenz (chaos, “Deterministic Nonperiodic Flow,” 1963); Stephen Smale (horseshoe map, 1967)
•	Core claim: Nonlinear deterministic systems can exhibit unpredictable behavior; long-term prediction is structurally limited in chaotic regimes
•	Convergence patterns: C05 (criticality/edge of chaos — systems at the boundary between order and chaos), C10 (fractal strange attractors), C23 (attractors as the organizing structure of dynamics), C21 (emergence — complex behavior from simple deterministic rules)
•	Independence check: Independent — Poincaré studied the three-body problem; Lorenz was a meteorologist; Smale a topologist. Different starting points, same phenomena
•	Claim tier: T1 — chaos is mathematically proven and empirically observed (weather, turbulence, cardiac rhythms). Specific applications vary in confidence
•	Key tension: Deterministic chaos vs. quantum indeterminacy — are they related or completely separate sources of unpredictability? Unresolved
•	Canonical text: Strogatz, Nonlinear Dynamics and Chaos (1994), Ch. 1-2 on flows on the line and bifurcations

## 2.3 Biology

Evolution by Natural Selection

•	Founder(s): Charles Darwin (On the Origin of Species, 1859); Alfred Russel Wallace (“On the Tendency of Varieties to Depart Indefinitely From the Original Type,” 1858)
•	Core claim: Populations change over time because heritable variation in traits causes differential survival and reproduction
•	Convergence patterns: C09 (selection + variation + retention — the evolutionary algorithm), C07 (feedback: adaptive traits increase in frequency, changing the selection pressure), C16 (branching tree of life as optimal exploration of phenotype space), C21 (emergence: complex adaptations from cumulative selection)
•	Independence check: Independent — Darwin and Wallace were naturalists studying biogeography and breeding, not physicists or mathematicians
•	Claim tier: T0 — evolution is observed in real time (antibiotic resistance, peppered moths, Darwin’s finches). Common ancestry confirmed by molecular genetics
•	Key tension: Gradualism vs. punctuated equilibrium; adaptationism vs. constraint-based views. Also: natural selection is not C02 (least action) — evolution is myopic, not optimal
•	Canonical text: Darwin, On the Origin of Species (1859), Ch. 3-4 on the struggle for existence and natural selection

Modern Synthesis

•	Founder(s): Gregor Mendel (laws of inheritance, 1865, rediscovered 1900); Ronald Fisher (The Genetical Theory of Natural Selection, 1930); J.B.S. Haldane (cost of selection, 1927); Sewall Wright (shifting balance, 1931); Theodosius Dobzhansky (Genetics and the Origin of Species, 1937); Ernst Mayr (Systematics and the Origin of Species, 1942)
•	Core claim: Evolution is the change in allele frequencies in populations, driven by mutation, selection, drift, and gene flow
•	Convergence patterns: C09 (population genetics formalizes selection-variation-retention), C15 (optimization: Fisher’s fundamental theorem shows natural selection increases mean fitness), C10 (neutral theory shows molecular evolution has scale-invariant properties), C21 (speciation as emergence of reproductive isolation)
•	Independence check: Mendel was a monk doing pea experiments. Fisher, Haldane, Wright were mathematicians/statisticians bringing formal rigor. Independent of physics
•	Claim tier: T0 — population genetics is experimentally confirmed; the synthesis is the operating framework of all biology
•	Key tension: Neutral theory (Kimura, 1968) vs. selectionism — most molecular change may be non-adaptive. Also: gene-centric vs. multilevel selection (group selection) remains disputed
•	Canonical text: Dobzhansky, Genetics and the Origin of Species (1937), Ch. 1-3 on genetic variation in populations

Molecular Biology

•	Founder(s): James Watson & Francis Crick (double helix structure, 1953); Francis Crick (central dogma, 1958); Marshall Nirenberg & Heinrich Matthaei (genetic code, 1961)
•	Core claim: Genetic information is stored in the sequence of DNA bases; it flows DNA→RNA→protein (central dogma); this information controls cellular function and development
•	Convergence patterns: C06 (information: the genetic code is literally a code, mapping 64 codons to 20 amino acids), C08 (self-reference: DNA contains instructions for its own replication machinery), C12 (autopoiesis: cells self-produce), C20 (the genetic code as a computational system — transcription/translation as algorithm)
•	Independence check: Independent — Watson and Crick used X-ray crystallography (Franklin, Wilkins) and model-building, not evolutionary theory or physics
•	Claim tier: T0 — DNA sequencing, CRISPR, genetic engineering all confirm the framework
•	Key tension: Central dogma (information flows one way) has exceptions — reverse transcriptase, prions. Also: the “gene” as a discrete unit is challenged by alternative splicing, epigenetics, and regulatory networks
•	Canonical text: Watson et al., Molecular Biology of the Gene (7th ed., 2013), Ch. 1-3 on the structure and function of DNA

Evolutionary Development (Evo-Devo)

•	Founder(s): Sean Carroll (Endless Forms Most Beautiful, 2005); Mary Jane West-Eberhard (Developmental Plasticity and Evolution, 2003); earlier: Ernst Haeckel, Gavin de Beer. Key gene: Hox genes discovered by Lewis, Nüsslein-Volhard, Wieschaus (Nobel 1995)
•	Core claim: Evolutionary change is largely driven by alterations in developmental gene regulatory networks, not just coding sequence changes
•	Convergence patterns: C09 (selection acts on developmental programs), C10 (Hox genes and other toolkit genes are deeply conserved — scale invariance across phyla), C21 (emergence: morphological diversity from combinatorial use of conserved toolkit), C08 (modularity and recursion: gene regulatory networks have recursive hierarchical structure)
•	Independence check: Independent — emerged from developmental biology (embryology) and molecular genetics, converging with evolutionary theory. Different starting point from population genetics
•	Claim tier: T1 — Hox gene conservation and cis-regulatory evolution are well-established. Claims about developmental plasticity driving evolution (West-Eberhard) are more debated
•	Key tension: Evo-devo challenges the modern synthesis’ gene-centric view — regulatory evolution may be more important than coding changes. Also: how much does plasticity drive vs. respond to selection? Active research area
•	Canonical text: Carroll, Endless Forms Most Beautiful (2005), Ch. 3-4 on the genetic toolkit for development

Ecological Systems

•	Founder(s): Alfred Lotka (Elements of Physical Biology, 1925); Vito Volterra (predator-prey equations, 1926); Eugene Odum (Fundamentals of Ecology, 1953); Howard Odum (energetics of ecosystems)
•	Core claim: Ecosystems are networks of energy and nutrient flows among populations; population dynamics are governed by coupled differential equations with feedback
•	Convergence patterns: C07 (feedback/homeostasis: predator-prey cycles, carrying capacity), C11 (networks: food webs as ecological networks), C05 (criticality: ecosystems at the edge of stability), C19 (thermoeconomics: energy flow through trophic levels mirrors economic production)
•	Independence check: Independent — Lotka was a physical chemist; Volterra a mathematician; the Odums were ecologists. Converged from different directions
•	Claim tier: T1 — Lotka-Volterra equations describe simple systems well; real ecosystems are more complex. Food web theory is established; claims about ecosystem self-regulation are more speculative
•	Key tension: Equilibrium ecology (Clements, Odum) vs. non-equilibrium ecology (Gleason, disturbance regimes). Are ecosystems organized superorganisms or random assemblages? Still debated
•	Canonical text: Lotka, Elements of Physical Biology (1925), Part II on interspecies competition

Assembly Theory

•	Founder(s): Lee Cronin & Sara Walker (“Quantifying Selection and Agency in Biology,” 2021; “Identifying Molecules as Biosignatures with Assembly Theory and Mass Spectrometry,” Nature Communications, 2021)
•	Core claim: The complexity of an object can be measured by its minimal assembly steps from elementary building blocks; high “assembly index” indicates selection (not random chemistry)
•	Convergence patterns: C09 (selection increases assembly index — selection is the process that builds complexity), C12 (autopoiesis: living systems are self-assembling), C06 (information: assembly index as a measure of embodied information), C20 (computation: assembly as a computational process)
•	Independence check: Independent — Cronin is a chemist working on origins of life; Walker is an astrobiologist. The theory emerged from mass spectrometry of molecular complexity, not from traditional biology
•	Claim tier: T2 — experimental validation exists for molecules (mass spec detection). Application to life detection (biosignatures) is promising but unproven. Claims about “agency” and “selection” as formal measures are ambitious and contested
•	Key tension: Critics argue assembly theory is a reformulation of Kolmogorov complexity (C06) in chemical disguise, not a new principle. Also: the cutoff between “abiotic” and “biotic” assembly index is arbitrary
•	Canonical text: Cronin & Walker, “Identifying Molecules as Biosignatures with Assembly Theory and Mass Spectrometry,” Nature Communications 12, 3035 (2021)

## 2.4 Thermodynamics & Dissipative Structures

The Entropy Framework

•	Founder(s): Rudolf Clausius (2nd law, 1865: “Die Entropie der Welt strebt einem Maximum zu”); Ludwig Boltzmann (S = k log W, 1877); J. Willard Gibbs (statistical ensembles, 1902); Max Planck (blackbody radiation as entropy maximization, 1900)
•	Core claim: Entropy is a measure of microscopic disorder; isolated systems evolve toward maximum entropy; the arrow of time is thermodynamic
•	Convergence patterns: C01 (gradient dissipation — entropy production requires gradient dissipation), C06 (entropy as information — Boltzmann’s formula equates entropy with missing microscopic information), C07 (equilibrium as homeostatic maximum entropy state)
•	Independence check: Clausius was an engineer-physicist; Boltzmann was a theoretical physicist; Gibbs was a mathematician. Independent traditions converging on the same concept
•	Claim tier: T0 — statistical mechanics is confirmed daily in every chemical reaction, heat engine, and refrigerator
•	Key tension: Boltzmann’s H-theorem assumes molecular chaos (Stosszahlansatz), which is time-asymmetric. Loschmidt’s paradox: how can time-asymmetric macro-behavior emerge from time-symmetric micro-dynamics? Still debated
•	Canonical text: Boltzmann, Lectures on Gas Theory (1896-98), Part I, Ch. 1-3 on the H-theorem

Open Systems & Negentropy

•	Founder(s): Erwin Schrödinger (What is Life?, 1944); preceded by Ludwig von Bertalanffy (open systems theory, 1940)
•	Core claim: Living organisms maintain order by exporting entropy to their environment — they feed on “negentropy” (negative entropy)
•	Convergence patterns: C01 (gradient dissipation: life requires energy gradients to maintain order), C07 (homeostasis: living systems maintain steady states far from equilibrium), C12 (autopoiesis: self-maintenance through entropy export)
•	Independence check: Schrödinger was a quantum physicist asking a biological question; Bertalanffy was a biologist. Independent starting points
•	Claim tier: T1 — the concept is qualitatively correct but “negentropy” is not a well-defined physical quantity. Free energy (Gibbs/Helmholtz) is the rigorous measure
•	Key tension: Schrödinger’s negentropy is thermodynamically imprecise — life consumes free energy, not entropy per se. Also: the concept conflates information entropy (Shannon) with thermodynamic entropy (Clausius)
•	Canonical text: Schrödinger, What is Life? (1944), Ch. 6 on “Order, Disorder and Entropy”

Dissipative Structures

•	Founder(s): Ilya Prigogine & Paul Glansdorff (“Thermodynamic Theory of Structure, Stability and Fluctuations,” 1971); Gregoire Nicolis & Ilya Prigogine (Self-Organization in Nonequilibrium Systems, 1977)
•	Core claim: Far from equilibrium, open systems can spontaneously form ordered structures sustained by continuous energy/matter flow — dissipation creates order
•	Convergence patterns: C01 (gradient dissipation is the driver), C05 (criticality: dissipative structures form at bifurcation points), C07 (feedback: autocatalytic cycles maintain structure), C12 (self-organization as proto-autopoiesis)
•	Independence check: Prigogine started from chemical thermodynamics and kinetics, not biology. The application to living systems came after the formal theory
•	Claim tier: T1 — Bénard cells, BZ reactions, and Turing patterns confirm the general principle. Application to living cells and organisms is more interpretive
•	Key tension: Dissipative structure theory claims dissipation is the source of order; this conflicts with equilibrium thermodynamics where dissipation destroys order. The resolution (far-from-equilibrium) is correct but the rhetoric sometimes overreaches
•	Canonical text: Nicolis & Prigogine, Self-Organization in Nonequilibrium Systems (1977), Ch. 7-9 on chemical instabilities and dissipative structures

Maximum Entropy Production (MEP)

•	Founder(s): Rod Dewar (“Maximum Entropy Production and the Fluctuation Theorem,” J. Phys. A, 2005); Leonid Martyushev & Vladimir Seleznev (“Maximum Entropy Production Principle in Physics, Chemistry and Biology,” Physics Reports, 2006); earlier: Paltridge (minimum entropy exchange, 1975) and Sawada
•	Core claim: Non-equilibrium systems evolve to states that maximize the rate of entropy production, subject to constraints
•	Convergence patterns: C01 (gradient dissipation — MEP selects the fastest dissipating path), C02 (least action — MEP is a variational principle for non-equilibrium systems), C15 (optimization: entropy production rate as the quantity being maximized)
•	Independence check: Independent — Dewar used Jaynes’ maximum entropy inference; Martyushev came from non-equilibrium thermodynamics. Converged on similar principles
•	Claim tier: T2 — confirmed in some Earth systems (zonal climate structure, river networks) and crystal growth. General proof remains lacking. Critics argue MEP is a selection effect, not a physical law
•	Key tension: MEP vs. minimum entropy production (Prigogine’s linear regime result). These are contradictory: which regime applies when? The boundary between them is not well-defined
•	Canonical text: Dewar, “Maximum Entropy Production and the Fluctuation Theorem,” Journal of Physics A 38, L371 (2005)

Constructal Law

•	Founder(s): Adrian Bejan (Shape and Structure, from Engineering to Nature, 1997; “Constructal Theory of Organization in Nature,” International Journal of Heat and Mass Transfer, 1997)
•	Core claim: For a finite-size flow system to persist in time, it must evolve to provide greater access to its currents; it generates a configuration that provides easier flow
•	Convergence patterns: C01 (gradient dissipation: the law describes how flow systems minimize resistance), C16 (branching/optimal transport: river deltas, lungs, city traffic all show tree-like structures), C10 (scale invariance: constructal patterns appear at all scales), C17 (spirals and tree-like structures as optimal flow configurations)
•	Independence check: Independent — Bejan is a mechanical engineer who studied heat transfer and fluid mechanics. The generalization to all of nature came later
•	Claim tier: T2 — successfully predicts many observed flow configurations (river basins, bronchial trees, street networks). Critics argue it’s a restatement of optimization principles, not a new law of thermodynamics
•	Key tension: Constructal law claims to be a universal law of physics; critics say it’s an engineering optimization principle dressed in physical language. The status as “law” vs. “design principle” is disputed
•	Canonical text: Bejan & Lorente, “The Constructal Law and the Evolution of Design in Nature,” Physics of Life Reviews 8, 209 (2011)

Dissipation-Driven Adaptation

•	Founder(s): Jeremy England (“Statistical Physics of Adaptation and Self-Replication,” J. Chem. Phys., 2013; Every Life Is on Fire, 2020); building on Hatano & Sasa (steady-state thermodynamics, 2001) and Jarzynski (nonequilibrium fluctuation relations, 1997)
•	Core claim: Strongly driven systems will spontaneously tune to states that absorb and dissipate work efficiently; adaptation to the environment is a thermodynamic tendency
•	Convergence patterns: C01 (gradient dissipation: the driving force), C09 (selection: dissipation selects for stable configurations), C12 (autopoiesis: self-replicators are efficient dissipators), C25 (teleology: the appearance of purpose from thermodynamics)
•	Independence check: Independent — England is a physicist who applied nonequilibrium statistical mechanics to molecular dynamics. The connection to life was a theoretical prediction, not biological fieldwork
•	Claim tier: T2 — simulation evidence exists (molecular dynamics of driven systems showing structure formation). Experimental confirmation of specific claims about self-replication is preliminary. The book (Every Life Is on Fire) makes stronger claims than the papers
•	Key tension: Critics (e.g., Goldenfeld, Woese) argue that dissipation-driven adaptation explains structure but not the specific information-rich structures of life. Also: the theory says nothing about the genetic code, metabolism, or heredity. Risk of “physics imperialism”
•	Canonical text: England, “Statistical Physics of Adaptation and Self-Replication,” Journal of Chemical Physics 139, 121923 (2013)

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