About Entropy as a Phenomenon

Entropy is a concept used in physical sciences and information theory. It is a property of a physical system or data string consisting of a great number of elements. Entropy is related to amount of disorder, complexity, or unpredictability of the system.

Take a classroom of noisy restless school children waiting for the teacher to start the lesson. Should you have a microphone coupled to a computer calculating the entropy of the recorded signals, it would drop from a high to low value just at the moment when the teacher enters the room.

Entropy in Nature

Typically molecules of gases or liquids are used to illustrate the entropy in nature. Molecules of water in liquid form have more freedom to move around each other than the same molecules in ice. Entropy is also related to the temperature or energy of the system.

The entropy of water is higher than that of ice and decreases gradually when cooled down, but just when the water changes to ice The entropy drops suddenly because of phase transition from a liquid state to a solid state.

Entropy Versus Chaos

Entropy and chaos can easily be interpreted as having the same meaning. lt seems that there should be lot of disordering chaotic system. However, mathematically speaking there is order in chaotic systems in the sense that the same kind of patterns can be found repeatably when looking at the system in different scales.

Geometric structures which copy themselves in smaller and smaller details are called fractals. If you calculate the fractal exponent of the system, it is closely related to the entropy.

Shannon’s Entropy

When applied in information theory and signal analysis, the irregularity (complexity, unpredictability) characteristics of any given signal can be described by using entropy. A signal that consists of a wide spread of frequencies has higher entropy than a signal that has only few frequencies.

Thus, signal complexity is quite an intuitive description. Shannon’s Entropy is an invariant measure which allows comparison between Different signals, because it is insensitive to absolute measure such As frequency and amplitude.

Anesthesia and Entropy

It is well known that anesthetic drugs have a potent effect on the brain cell system. The state of the system can be measured on the skull surface by picking up the weak electrical EEG signals associated with the activity of the neurons.

The entropy of the EEG signal with in a certain time window can be calculated from the signal itself or its spectrum. Entropy of the signal has been shown to drop when a patient falls asleep and again increase when the patient wakes up.

Entropy Algorithm Description

H.E. Viertio-Oja
Includes a fully detailed description of the Entropy algorithm as applied in the GE Healthcare Entropy Module.

• pdf/221 KB

Sipectral Entropy, Approximate Entropy, Complexity and Bispectrum of EEG during Anesthesia

H.E. Viertio-Oja et al., Published in the MAAC Book of Abstracts
Presented at the 5th MAAC congress, 2001. Work rewarded by a Certificate of Achievement by the organizing committee.

• pdf/144 KB

Optimization of Response Time of Spectral EEG Entropy Enables Early Warning of Emergence from Unconsciousness

H.E. Viertjo-Oja et al., Published in the MAAC Book of Abstracts.
Presented at the 5th MAAC congress, 2001.

• pdf/221 KB

New method to determine depth of anesthesia from EEG measurements

H.E. Viertio-Oja et al., J CIin Monit Camp16 (2000) p. 60
Presented at the STA 2000 meeting. Absolute “transition levels” for fractal exponent, complexities, bispectral parameters and entropies are reported for the first time. Awarded Best Abstract by the Research Committee in the category Clinical Application of Technology.

• pdf/221 KB

• For further reading on Claude Shannon’s Mathematical Theory of Communication please visit:

• Claude Shannon’s Mathematical Theory of Communication

• For further reading on GE Healthcare’s Adequacy of Anesthesia concept, please visit:

• Our Clinical Window

• Or Our Product Portfolio:Adequacy of Anesthesia