The entropy of systems


  • J. L. Manriquez-Zepeda UAEMex
  • J. Rueda-Paz UAEMex
  • P. D. Filio-Aguilar UAEMex
  • L. López-García UAEMex



Von Neumann entropy, shannon entropy, information theory, history of entropy, systems and states, teaching entropy


The entropy concept is studied from the perspective of several formalisms. It is reviewed the origins of this in the classical thermodynamics. It also is developed a step-by-step-clearly demonstration about it. After that, it is connected this formula with the entropy of Shannon. Elementary concepts of the quantum mechanics are explained to demonstrate the von Neumann entropy formula. It is proposed the entropy concept as a measure of the variability into the distribution of the states of a system given a set of rules that operate inside it for a while. From the perspective of the information theory, a language reaches a configuration to be optimal for communications. In this way, systems and languages can be studied using the same concept of entropy. It is stressed the importance of the teaching of the entropy because this is useful in the development of new technologies, for example the quantum communications.


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How to Cite

J. L. Manriquez-Zepeda, J. Rueda-Paz, P. D. Filio-Aguilar, and L. López-García, “The entropy of systems”, Rev. Mex. Fis. E, vol. 20, no. 1 Jan-Jun, pp. 010211 1–, Jan. 2023.