On Thermodynamic Interpretation of Transfer Entropy

Entropy

Mikhail Prokopenko¹  Joseph T. Lizier¹ 

[1] CSIRO Information and Communications Technologies Centre, PO Box 76, Epping, NSW 1710, Australia; E-Mail:

关键词: transfer entropy;    information transfer;    entropy production;    irreversibility;    Kullback–Leibler divergence;    thermodynamic equilibrium;    Boltzmann’s principle;    causal effect;   

DOI  :  10.3390/e15020524

来源: mdpi

【 摘 要 】

We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.