Speculation on an Example of Maximization of Tsallis Entropy Subject to a Constraint Part 2 - Dual Probabilities and Frequency
Fuente:
Zenodo
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Recurso digital |
| Pubblicazione: |
Zenodo
2025
|
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866901090435334144 |
|---|---|
| author | Ruggeri, Francesco R. |
| author_facet | Ruggeri, Francesco R. |
| contents | <p> In Part I, we tried to provide an example of how Tsallis entropy would naturally arise from an example of a germinating seed. We focused mostly on the idea of creating a failure probability which could be maximized subject to an a priori constraint in order to find a distribution which represented a situation of maximum ignorance (which we considered equivalent to maximum entropy). This failure probability became the Tsallis entropy if one insisted that the q=1 case represent Maxwell-Boltzmann entropy.</p> <p> Here, we wish to examine the notion of f(ei) power q in more detail. In Part I, we noted that there seem to be two kinds of probabilities present, one represented by f(ei) and the second by f(ei) power q. In other words, there are two interrelated probabilities, with the second being an AND situation governed by q of the first. Here we argue that this suggests a frequency or cycling of one probability, namely f(ei) with f(ei) power q being linked with q cycles which reset themselves each time to allow for an AND expression f(ei) power q. </p> <p> In particular, we consider the case of a sunflower seed which readily germinates, but takes several (q) days to do so. We argue that this seed will germinate unless it is eaten by a bird or animal. Thus, the probability to germinate is tied to the probability for the seed not to be eaten. The issue is that the probability to be eaten, f1(ei), is tied to a cycle of a day because such a probability only holds for a day. If there are q successive days, then these are independent and the probability not to be eaten during the germination period is (1-f1(ei)) power q. Thus, we argue that the f(ei) power q term which appears in Tsallis entropy appears physically in the natural world and is linked to processes (germination) which occur over several cycle periods (q days) with a cycle be linked with a probability f1(ei). In other words, f(ei) only applies to the cycle period, hence the need for an AND product, f(ei) power q for a process which takes longer than a cycle period.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_14954589 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Speculation on an Example of Maximization of Tsallis Entropy Subject to a Constraint Part 2 - Dual Probabilities and Frequency Ruggeri, Francesco R. <p> In Part I, we tried to provide an example of how Tsallis entropy would naturally arise from an example of a germinating seed. We focused mostly on the idea of creating a failure probability which could be maximized subject to an a priori constraint in order to find a distribution which represented a situation of maximum ignorance (which we considered equivalent to maximum entropy). This failure probability became the Tsallis entropy if one insisted that the q=1 case represent Maxwell-Boltzmann entropy.</p> <p> Here, we wish to examine the notion of f(ei) power q in more detail. In Part I, we noted that there seem to be two kinds of probabilities present, one represented by f(ei) and the second by f(ei) power q. In other words, there are two interrelated probabilities, with the second being an AND situation governed by q of the first. Here we argue that this suggests a frequency or cycling of one probability, namely f(ei) with f(ei) power q being linked with q cycles which reset themselves each time to allow for an AND expression f(ei) power q. </p> <p> In particular, we consider the case of a sunflower seed which readily germinates, but takes several (q) days to do so. We argue that this seed will germinate unless it is eaten by a bird or animal. Thus, the probability to germinate is tied to the probability for the seed not to be eaten. The issue is that the probability to be eaten, f1(ei), is tied to a cycle of a day because such a probability only holds for a day. If there are q successive days, then these are independent and the probability not to be eaten during the germination period is (1-f1(ei)) power q. Thus, we argue that the f(ei) power q term which appears in Tsallis entropy appears physically in the natural world and is linked to processes (germination) which occur over several cycle periods (q days) with a cycle be linked with a probability f1(ei). In other words, f(ei) only applies to the cycle period, hence the need for an AND product, f(ei) power q for a process which takes longer than a cycle period.</p> <p> </p> |
| title | Speculation on an Example of Maximization of Tsallis Entropy Subject to a Constraint Part 2 - Dual Probabilities and Frequency |
| url | https://doi.org/10.5281/zenodo.14954589 |