Physical Systems and Laws

Physical laws in classical physics have are deterministic in nature which implies that any isolated system such as the universe as a whole evolves in a deterministic way so that once we know the state of a system at a time states of the system in future will be uniquely predicted. This turns out to be violated by the uncertainty principle of quantum mechanics on the one hand and the presence of chaotic motion even in classical physics on the other. The energy conservation law and the law of increase of entropy are discussed in an elementary way. They are valid for any isolated system without exceptions, showing the universality and great power of laws of physics. Symmetry principle is an indispensable ingredient in modern physics. Symmetries such as the symmetry under translations in space or time are well shared by the fundamental laws of physics, which lead to the law of energy conservation or momentum conservation. Also the charge conservation law is related to the gauge symmetry of electromagnetic interaction. The special and general relativities by Einstein based upon the geometrical symmetry principle revealed the space-time structure of the physical world with remarkable outcomes. For example, space and time are interrelated, mass is a kind of energy, and gravity is related to the curvature of the space-time structure of our physical world. Ordinary matter consists of a huge number of atoms or molecules and there exist quite many microscopic states indistinguishable from each other. Thus, we need a statistical approach to find useful information about ordinary matter. Statistical thermodynamics is such a theory to connect the microscopic and macroscopic worlds. The basic postulate is that every microstate is realized with equal probability for an isolated system. This postulate together with the first and second laws of thermodynamics makes it possible to predict properties of any thermodynamical quantity not only for isolated systems but also for other systems interacting with their surroundings. Study of complex systems with non-linear interactions among their constituents is a relatively new field out of which some interesting features of the complex systems emerge. For example, even a system with a few degrees of freedom of motion can exhibit chaotic behavior under appropriate conditions. Important concepts in complex phenomena such as attractors, bifurcations, entrainments, fractals, and chaos are described.