In discrete systems, such as Markov chains, Shannon entropy can be used to explain the uncertainty and complexity of the system. In continuous systems, such as pure jump Markov processes, does the corresponding differential entropy have a clear physical meaning? If so, how can differential entropy be used to interpret continuous systems?
Sikander Ali
Information Theory: Quantifies average uncertainty or information per unit of the variable. Thermodynamics: Related to thermodynamic entropy, which measures disorder in physical systems. Signal Processing: Indicates the bandwidth or information content of signals. Statistical Mechanics: Connects to the volume of phase space occupied by a system.
Yes, differential entropy measures the uncertainty or randomness in a continuous probability distribution. It has physical meanings in:
Yes, differential entropy in continuous systems, such as pure jump Markov processes, does have physical and interpretative significance, though it differs from Shannon entropy in discrete systems. Here’s how differential entropy can be used to interpret continuous systems:
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