In this part we introduce the foundations of Statistical Physics, focusing on how collective macroscopic behavior emerges from the microscopic dynamics of many-particle systems. The course develops the conceptual framework connecting probability, thermodynamics, and mechanics, providing a bridge between microscopic physical laws and observable material properties.
We begin by examining the statistical description of systems with many degrees of freedom and introduce core concepts such as microstates, macrostates, entropy, and probability distributions. The formulation of statistical ensembles—including the microcanonical, canonical, and grand canonical ensembles—is developed systematically, together with their connections to thermodynamic quantities such as temperature, free energy, and chemical potential.
Special attention is given to understanding fluctuations, phase transitions, and collective phenomena, which form the basis for modern condensed matter and soft matter physics. Simple model systems such as ideal gases, paramagnets, lattice models, and interacting particle systems are used to illustrate how universal behavior can emerge from microscopic interactions.
Where possible, emphasis is placed on building physical intuition alongside mathematical formulation. The course highlights how statistical physics extends beyond equilibrium thermodynamics into modern topics such as non-equilibrium systems, active matter, biological physics, and complex systems. Computational approaches and numerical simulations are introduced as essential tools for exploring many-body behavior beyond analytical limits.
There are also important topics that are not covered in full detail here. Advanced field-theoretic methods, renormalization group techniques, quantum statistical mechanics, and strongly correlated many-body systems are reserved for more advanced courses. Similarly, modern developments in machine learning-driven statistical inference and large-scale simulations will be introduced progressively in later modules.
This part aims to establish a strong conceptual and mathematical foundation for understanding collective phenomena across physics, chemistry, biology, and interdisciplinary complex systems.