Fundamentals and applications of statistical physics
Statistical physics bridges the gap between macroscopic and microscopic worlds, which originated in attempts to explain how the irreversible macroscopic behaviors can be reconciled with the reversible microscopic Hamiltonian equations of motion, in other words, why the entropy increases and how the direction of time arrow becomes certain. Statistical physics aims at a fundamental understanding of how the macroscopic collective properties emerge from interactions of many degrees of freedom, which cannot be simply deduced from an understanding of individuals. Representative examples of the emergent phenomena are phase transitions and criticalities, associated with singularities of thermodynamic functions, which signals the existence of universal physical mechanism underlying seemingly quite distinct systems. Contrary to other disciplines of physics, the scope of statistical physics is not restricted to specific systems but is rather unlimited and has found applications in broad areas, with considerable success, encompassing from solid-liquid-gas transitions of classical systems to macroscopic quantum effects such as superconductivity and superfluidity.
As stated above, we have witnessed the great triumphs of the equilibrium statistical physics in the 20th century. In this new era, the biggest challenges remained largely unexplored in the statistical physics are constructions of fundamental theories of nonequilibrium statistical mechanics and applications of statistical mechanics to realms beyond the traditional boundaries including social sciences and biological sciences. This defines the identity of us and what we explore: Based on statistical physics, we seek for theoretical understanding of fundamental principles underlying equilibrium or non-equilibrium behaviors of various systems, ranging from criticalities in the bio-soft matter to nonequilibrium quantum systems.