On Thermodynamic Interpretation of Transfer Entropy
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 en...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-02-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/15/2/524 |
| _version_ | 1828113670361579520 |
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| author | Don C. Price Joseph T. Lizier Mikhail Prokopenko |
| author_facet | Don C. Price Joseph T. Lizier Mikhail Prokopenko |
| author_sort | Don C. Price |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T12:12:31Z |
| format | Article |
| id | doaj.art-2246d210dbf74303a618f32895206bcc |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:12:31Z |
| publishDate | 2013-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-2246d210dbf74303a618f32895206bcc2022-12-22T04:24:34ZengMDPI AGEntropy1099-43002013-02-0115252454310.3390/e15020524On Thermodynamic Interpretation of Transfer EntropyDon C. PriceJoseph T. LizierMikhail ProkopenkoWe 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.http://www.mdpi.com/1099-4300/15/2/524transfer entropyinformation transferentropy productionirreversibilityKullback–Leibler divergencethermodynamic equilibriumBoltzmann’s principlecausal effect |
| spellingShingle | Don C. Price Joseph T. Lizier Mikhail Prokopenko On Thermodynamic Interpretation of Transfer Entropy Entropy transfer entropy information transfer entropy production irreversibility Kullback–Leibler divergence thermodynamic equilibrium Boltzmann’s principle causal effect |
| title | On Thermodynamic Interpretation of Transfer Entropy |
| title_full | On Thermodynamic Interpretation of Transfer Entropy |
| title_fullStr | On Thermodynamic Interpretation of Transfer Entropy |
| title_full_unstemmed | On Thermodynamic Interpretation of Transfer Entropy |
| title_short | On Thermodynamic Interpretation of Transfer Entropy |
| title_sort | on thermodynamic interpretation of transfer entropy |
| topic | transfer entropy information transfer entropy production irreversibility Kullback–Leibler divergence thermodynamic equilibrium Boltzmann’s principle causal effect |
| url | http://www.mdpi.com/1099-4300/15/2/524 |
| work_keys_str_mv | AT doncprice onthermodynamicinterpretationoftransferentropy AT josephtlizier onthermodynamicinterpretationoftransferentropy AT mikhailprokopenko onthermodynamicinterpretationoftransferentropy |