Origin of randomness in physical systems

Classical mechanics is a deterministic theory, in which the time evolution is uniquely determined for any given initial condition by the Newton equations (1.98). In quantum mechanics, the physical information associated with a given wave-function has an inherent probabilistic character, however the wavefiinction itself is rmiquely determined, again from any given initial wavefunction, by the Schrodinger equation (1.109). Nevertheless, many processes in nature appear to involve a random component in addition to their systematic evolution. What is the origin of this random character There are two answers to this question, both related to the way we observe physical systems  

We use a reduced description of the system (or process) of interest. In many cases, we seek simplified descriptions of physical processes by focusing on a small subsystem or on a few observables that characterize the process of interest. These observables can be macroscopic, for example, the energy, pressure, temperature, etc., or microscopic, for example, the center of mass position, a particular bond length, or the internal energy of a single molecule. In the reduced space of these important observables, the microscopic influence of the other 10 degrees of 

The correlation distance rcor for p (r) is defined as the distance above which p (r) and p (r+n cor) are statistically independent (n is a unit vector in any direction). 

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Physical observables as random variables 1.5.1 Origin of randomness in physical systems... 

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