**Appendix C: Detailed Graph Data (Edges)** **C.4.1: Edges Originating from Thermodynamics (Thermo) Nodes:** | Source Node ID | Target Node ID | Type | Rationale | Conf. | Dir. | |:-------------------------- |:-------------------------- |:----- |:-------------------------------------------------------------------------------------------------------------------------------------- |:---- |:--- | | `Thermo` | `StatMech` | `E-XPBY` | The macroscopic laws of thermodynamics are explained by the statistical behavior of microscopic constituents described by statistical mechanics. | M/H | D | | `Thermo` | `Concept::Energy` | `F-BAS`| Thermodynamics is fundamentally concerned with energy, its forms (heat, work), and its conservation (First Law). | H | D | | `Thermo` | `Concept::Entropy` | `F-BAS`| Thermodynamics introduces entropy as a key state variable governing spontaneity and equilibrium (Second, Third Laws). | H | D | | `Thermo::ZerothLaw` | `Thermo` | `S-COMP`| The Zeroth Law is a foundational principle defining thermal equilibrium within thermodynamics. | H | D | | `Thermo::FirstLaw` | `Thermo` | `S-COMP`| The First Law is a core principle of thermodynamics, stating energy conservation. | H | D | | `Thermo::FirstLaw` | `Concept::Energy` | `L-ENT`| The First Law is a specific application/statement of the general principle of energy conservation to thermodynamic systems. | H | D | | `Thermo::SecondLaw` | `Thermo` | `S-COMP`| The Second Law is a core principle of thermodynamics, defining entropy increase and the direction of spontaneous processes. | H | D | | `Thermo::SecondLaw` | `Thermo::Entropy` | `L-ENT`| The Second Law is formulated in terms of the behavior of thermodynamic entropy. | H | D | | `Thermo::SecondLaw` | `ArrowOfTime` *(Concept needed)* | `E-XPL` | The Second Law provides the basis for the macroscopic thermodynamic arrow of time (irreversibility). | H | D | | `Thermo::SecondLaw` | `CM::Determinism` / `QM::UnitaryEvolution` | `F-CHL` | The irreversibility implied by the Second Law appears to conflict with the time-reversible nature of underlying micro-dynamics (Loschmidt’s paradox). | H | D | | `Thermo::ThirdLaw` | `Thermo` | `S-COMP`| The Third Law is a core principle concerning the behavior of entropy near absolute zero. | H | D | | `Thermo::ThirdLaw` | `Thermo::Entropy` | `L-ENT`| The Third Law makes specific statements about the limiting value of thermodynamic entropy. | H | D | | `Thermo::Entropy` | `Concept::Entropy` | `L-INST`| Thermodynamic entropy is a specific instance/measure of the broader concept of entropy, related to heat and macroscopic disorder. | H | D | | `Thermo::MacroscopicSystem` | `Thermo` | `F-BAS`| The laws of thermodynamics are formulated for and apply primarily to macroscopic systems near equilibrium. | H | D | **C.4.2: Edges Originating from Statistical Mechanics (StatMech) Nodes:** | Source Node ID | Target Node ID | Type | Rationale | Conf. | Dir. | |:---------------------------- |:-------------------------- |:----- |:-------------------------------------------------------------------------------------------------------------------------------------- |:---- |:--- | | `StatMech` | `Thermo` | `E-RED`| Statistical mechanics provides a microscopic foundation aiming to reduce thermodynamic laws to statistical behavior of constituents. | M/H | D | | `StatMech` | `CM` / `QM` | `F-BAS`| Statistical mechanics applies statistical methods to the underlying microscopic dynamics described by either classical or quantum mechanics. | H | D | | `StatMech` | `Math::ProbabilityTheory` | `F-BAS`| Statistical mechanics fundamentally relies on probability theory and statistical ensembles to calculate macroscopic properties. | H | D | | `StatMech::BoltzmannEntropy` | `StatMech` | `S-COMP`| Boltzmann’s entropy formula is a core definition within statistical mechanics linking entropy to microstate count. | H | D | | `StatMech::BoltzmannEntropy` | `Thermo::Entropy` | `S-FORM`/`E-XPL`| Provides a microscopic interpretation intended to correspond to thermodynamic entropy for isolated systems in equilibrium. | H | D | | `StatMech::BoltzmannEntropy` | `StatMech::Microstate` | `F-BAS`| Boltzmann entropy is defined based on the number (W or Ω) of accessible microstates. | H | D | | `StatMech::GibbsEntropy` | `StatMech` | `S-COMP`| Gibbs’ entropy formula is a core definition within statistical mechanics for ensembles described by probability distributions. | H | D | | `StatMech::GibbsEntropy` | `Thermo::Entropy` | `S-FORM`/`E-XPL`| Provides a more general microscopic interpretation intended to correspond to thermodynamic entropy. | H | D | | `StatMech::GibbsEntropy` | `InfoSci::ShannonEntropy` | `S-FORM`/`E-ANL`| Gibbs entropy has the identical mathematical form as Shannon entropy, indicating a deep formal analogy. | H | S | | `StatMech::Microstate` | `StatMech` | `S-COMP`| The concept of microstates is fundamental to the statistical mechanics approach. | H | D | | `StatMech::Macrostate` | `StatMech` | `S-COMP`| The concept of macrostates (defined by macroscopic variables) is fundamental to linking micro and macro descriptions. | H | D | | `StatMech::Macrostate` | `StatMech::Microstate` | `S-ABS`| A macrostate is an abstraction corresponding to a large ensemble of possible microstates. | H | D | | `StatMech::ProbabilisticAssumption` | `StatMech` | `F-BAS`| Assumptions like equal a priori probabilities or ergodicity are necessary methodological components for standard statistical mechanics calculations. | H | D | | `StatMech` | `Thermo::SecondLaw` | `E-XPL`| Statistical mechanics explains the Second Law as the overwhelming tendency for systems to evolve towards more probable macrostates (higher W or H). | H | D |