Here is the continuation of the expanded map of statistical mechanics: d. Einstein solids and specific heat anomaly 4. Fermi-Dirac statistics a. Pauli exclusion principle and antisymmetry b. Fermi energy and degeneracy pressure c. Sommerfeld expansion and low-temperature behavior d. Fermi liquid theory and quasiparticles B. Interpretations of probability 1. Classical probability a. Laplace's definition and principle of insufficient reason b. Kolmogorov axioms and measure theory c. Conditional probability and Bayes' theorem d. Law of large numbers and central limit theorem 2. Frequentist interpretation a. Relative frequency and long-run limit b. Objective probability and repeatability c. Confidence intervals and hypothesis testing d. Limitations and criticisms 3. Bayesian interpretation a. Subjective probability and degree of belief b. Prior and posterior probabilities c. Bayes' rule and updating beliefs d. Maximum entropy principle and information theory 4. Quantum probability a. Born rule and probability amplitudes b. Quantum logic and non-commutative probability c. Quantum Bayesianism and subjective interpretation d. Many-worlds interpretation and branching probabilities C. Foundations of thermodynamics 1. Carnot's work a. Carnot cycle and efficiency b. Carnot's theorem and reversibility c. Caloric theory and heat as a substance d. Limitations and historical context 2. Clausius and entropy a. Mechanical equivalent of heat and first law b. Clausius inequality and second law c. Entropy as a state function and thermodynamic potential d. Principle of maximum entropy and equilibrium 3. Kelvin and the absolute temperature scale a. Kelvin's statements of the second law b. Absolute zero and unattainability principle c. Thermodynamic temperature and ideal gas scale d. Negative temperatures and spin systems 4. Gibbs and the thermodynamic potentials a. Legendre transforms and thermodynamic variables b. Gibbs free energy and chemical potential c. Maxwell relations and reciprocity d. Stability criteria and Le Chatelier's principle D. Philosophical issues 1. Reductionism and emergent properties a. Microstate and macrostate descriptions b. Supervenience and multiple realizability c. Emergent phenomena and complex systems d. Limitations of reductionist approaches 2. Arrow of time and irreversibility a. Time-reversal symmetry and microscopic laws b. Entropy increase and second law of thermodynamics c. Past hypothesis and initial conditions d. Cosmological arrow and anthropic reasoning 3. Maxwell's demon and information theory a. Szilard engine and entropy reduction b. Landauer's principle and information erasure c. Thermodynamics of computation and reversible computing d. Quantum Maxwell's demon and feedback control 4. Quantum measurement problem a. Wave function collapse and Born rule b. Decoherence and einselection c. Quantum-to-classical transition and emergent classicality d. Interpretations of quantum mechanics and reality IX. Current Research Frontiers A. Quantum thermodynamics 1. Quantum heat engines a. Otto cycle and quantum adiabatic processes b. Carnot efficiency and quantum limits c. Quantum refrigerators and heat pumps d. Quantum Otto engines and many-body effects 2. Quantum fluctuation theorems a. Jarzynski equality and nonequilibrium work relations b. Crooks fluctuation theorem and time-reversal symmetry c. Quantum work and two-point measurement scheme d. Quantum fluctuation relations and entropy production 3. Quantum coherence and correlations a. Quantum discord and non-classical correlations b. Quantum entanglement and thermodynamic efficiency c. Quantum coherence and thermodynamic constraints d. Quantum advantage and metrological applications 4. Quantum thermal machines a. Absorption refrigerators and heat-driven engines b. Quantum dots and single-electron devices c. Superconducting circuits and quantum annealers d. Optomechanical systems and nanoscale heat transport B. Active matter and biological systems 1. Flocking and swarming a. Vicsek model and self-propelled particles b. Alignment interactions and collective motion c. Phase transitions and orientational order d. Hydrodynamic theories and continuum descriptions 2. Active Brownian particles a. Self-propulsion and persistent motion b. Rotational diffusion and angular fluctuations c. Motility-induced phase separation and clustering d. Rectification and directed transport 3. Cytoskeletal dynamics a. Actin filaments and polymerization kinetics b. Microtubules and dynamic instability c. Motor proteins and active force generation d. Contractility and stress fibers 4. Collective behavior in living systems a. Bacterial colonies and quorum sensing b. Insect societies and division of labor c. Bird flocks and fish schools d. Human crowds and social dynamics C. Machine learning and data-driven approaches 1. Neural networks for potential energy surfaces a. Feedforward neural networks and backpropagation b. Behler-Parrinello networks and atom-centered symmetry functions c. Deep potential molecular dynamics and transferability d. Gaussian approximation potentials and kernel methods 2. Generative models for molecular design a. Variational autoencoders and latent space sampling b. Generative adversarial networks and objective functions c. Reinforcement learning and reward shaping d. Inverse molecular design and property optimization 3. Reinforcement learning for materials discovery a. Markov decision processes and value functions b. Q-learning and temporal difference methods c. Policy gradients and actor-critic algorithms d. Materials screening and high-throughput experimentation 4. Compressed sensing and sparse sampling a. Sparsity and L1 regularization b. Basis pursuit and matching pursuit algorithms c. Matrix completion and low-rank approximations d. Phase retrieval and diffraction imaging D. Quantum simulation and quantum computing 1. Cold atom systems a. Optical lattices and Hubbard models b. Feshbach resonances and interaction control c. Quantum gas microscopes and single-site resolution d. Synthetic gauge fields and topological phases 2. Superconducting qubits a. Josephson junctions and circuit QED b. Transmon qubits and flux qubits c. Quantum gates and circuit optimization d. Quantum error correction and surface codes 3. Trapped ions a. Paul traps and Coulomb crystals b. Hyperfine states and optical transitions c. Raman lasers and entangling gates d. Quantum simulations and many-body physics 4. Quantum algorithms for statistical mechanics a. Quantum phase estimation and thermal states b. Quantum Metropolis sampling and Gibbs states c. Quantum annealing and adiabatic optimization d. Variational quantum eigensolvers and hybrid algorithms E. Non-equilibrium quantum dynamics 1. Quantum quenches a. Sudden quenches and excitation dynamics b. Kibble-Zurek mechanism and defect formation c. Dynamical phase transitions and order parameters d. Thermalization and eigenstate thermalization hypothesis 2. Floquet engineering a. Periodic driving and Floquet theory b. High-frequency expansions and effective Hamiltonians c. Floquet topological insulators and Floquet-Bloch states d. Floquet prethermalization and heating 3. Many-body localization a. Anderson localization and disorder b. Absence of thermalization and memory effects c. Local integrals of motion and emergent integrability d. Delocalization transitions and critical properties 4. Quantum thermalization and eigenstate thermalization hypothesis a. Quantum chaos and level statistics b. Typicality and canonical ensembles c. Entanglement entropy and volume law scaling d. Exceptions and integrable systems X. Interdisciplinary Connections A. Information theory and computation 1. Landauer's principle a. Information erasure and entropy increase b. Szilard engine and Maxwell's demon c. Experimental demonstrations and limitations d. Quantum Landauer principle and entanglement 2. Algorithmic complexity and Kolmogorov complexity a. Turing machines and universal computation b. Kolmogorov complexity and algorithmic randomness c. Chaitin's Omega number and halting probability d. Algorithmic probability and Solomonoff induction 3. Quantum information theory a. Von Neumann entropy and quantum relative entropy b. Quantum data compression and Schumacher's theorem c. Quantum channel capacity and Holevo bound d. Quantum error correction and fault-tolerant computation 4. Quantum error correction and fault-tolerant computation a. Quantum noise and decoherence b. Quantum error-correcting codes and stabilizer formalism c. Threshold theorem and concatenated codes d. Topological quantum computation and anyonic braiding B. Econophysics and social systems 1. Financial markets a. Random walk hypothesis and efficient market hypothesis b. Black-Scholes model and option pricing c. Volatility clustering and GARCH models d. Econophysics and statistical properties of financial time series 2. Wealth distribution a. Pareto distribution and power laws b. Gibrat's law and multiplicative processes c. Agent-based models and wealth condensation d. Inequality measures and Gini coefficient 3. Opinion dynamics a. Voter model and social influence b. Majority rule and consensus formation c. Bounded confidence models and opinion fragmentation d. Social impact theory and Latané model 4. Complex networks a. Small-world networks and Watts-Strogatz model b. Scale-free networks and preferential attachment c. Community detection and modularity optimization d. Epidemic spreading and percolation theory C. Neuroscience and brain dynamics 1. Neural networks a. McCulloch-Pitts model and firing rate neurons b. Hopfield networks and associative memory c. Feedforward networks and backpropagation learning d. Recurrent neural networks and dynamical systems 2. Attractor neural networks a. Point attractors and memory retrieval b. Continuous attractors and neural integrators c. Chaotic attractors and itinerant dynamics d. Attractor networks and cognitive functions 3. Criticality in brain dynamics a. Power-law distributions and scale-free behavior b. Avalanches and self-organized criticality c. Critical brain hypothesis and optimal information processing d. Functional connectivity and resting-state networks 4. Information processing in the brain a. Neural coding and spike trains b. Information theory and mutual information c. Efficient coding hypothesis and sparse coding d. Bayesian brain hypothesis and predictive coding D. Ecology and evolutionary dynamics 1. Population dynamics a. Lotka-Volterra equations and predator-prey systems b. Logistic growth and carrying capacity c. Allee effect and critical population size d. Metapopulations and spatial ecology 2. Evolutionary game theory a. Replicator dynamics and evolutionary stable strategies b. Hawk-dove game and frequency-dependent selection c. Prisoner's dilemma and cooperation d. Evolutionary dynamics on graphs and networks 3. Speciation and extinction a. Adaptive radiation and ecological niches b. Reproductive isolation and Dobzhansky-Muller incompatibilities c. Red Queen hypothesis and coevolutionary arms race d. Mass extinctions and biodiversity dynamics 4. Ecological networks a. Food webs and trophic levels b. Mutualistic networks and plant-pollinator interactions c. Nestedness and modularity in ecological networks d. Stability and robustness of ecosystems E. Quantum gravity and holography 1. AdS/CFT correspondence a. Anti-de Sitter space and conformal field theory b. Holographic principle and bulk-boundary duality c. Gravity/gauge duality and strong-weak coupling d. Applications in condensed matter and quantum information 2. Black hole thermodynamics a. Bekenstein-Hawking entropy and area law b. Hawking radiation and black hole evaporation c. Information paradox and firewall controversy d. Holographic entanglement entropy and Ryu-Takayanagi formula 3. Entanglement entropy a. Von Neumann entropy and reduced density matrix b. Area law and quantum many-body systems c. Entanglement spectrum and topological order d. Tensor networks and holographic entanglement entropy 4. Emergent spacetime a. Quantum entanglement and spacetime geometry b. ER=EPR conjecture and wormholes c. Tensor networks and holographic codes d. Quantum gravity and noncommutative geometry This expanded map provides a comprehensive overview of the vast field of statistical mechanics, covering fundamental concepts, advanced topics, historical perspectives, current research frontiers, and interdisciplinary connections. It highlights the richness and diversity of the field, showcasing its applications in various domains of physics and beyond. However, it is important to note that even this expanded map is not exhaustive, as the field of statistical mechanics continues to evolve and grow with new discoveries and developments.