Deterministic versus probabilistic models

A deterministic model can be used for a physical quantity and the process generating it provided sufficient information is available about the initial state and the dynamics of the process generating the physical quantity. For example,

• We can determine the position of a particle moving under a constant force if we know the initial position of the particle and the magnitude and the direction of the force.
                         
• We can determine the current in a circuit consisting of resistance, inductance and capacitance for a known voltage source applying Kirchoff's laws.

Many of the physical quantities are random in the sense that these quantities cannot be predicted with certainty and can be described in terms of probabilistic models only. For example,

• The outcome of the tossing of a coin cannot be predicted with certainty. Thus the outcome of tossing a coin is random.
                         
• The number of ones and zeros in a packet of binary data arriving through a communication channel cannot be precisely predicted is random.
                  
• The ubiquitous noise corrupting the signal during acquisition, storage and transmission can be modelled only through statistical analysis.