| _version_ | 1866901595860500480 |
|---|---|
| author | Ruggeri, Francesco R. |
| author_facet | Ruggeri, Francesco R. |
| contents | <p> The Maxwell-Boltzmann distribution is so closely linked to an ideal gas as well as to MaxEnt (maximum entropy subject to constraints) that one might associate properties of interactions in the gas with MaxEnt in general. We argue that MaxEnt solutions may exist which do not conform to the interactions of the ideal gas. In particular, we argue that for an ideal gas: p(ei)p(ej) = p(ei+ej) ((1)) for physical reasons and this relation automatically yields p(ei)=Cexp(-ei/T) or - Sum over i p(ei) ln(p(ei) for entropy. As a result, it might seem that maximum entropy subject to the constraints Sum over i p(ei)=1 and Sum over i ei p(ei) = Eave ((2)) is equivalent to ((1)). We argue here that this is only one case. Maximum entropy for the constraints ((2)) has two solutions, and only one corresponds to ((1)), namely F=ln(p) for entropy = - Sum over i p(ei) F(p(ei)). As a result, ln(p), the Maxwell-Boltzmann case of F is linked with one kind of maximization of entropy and certain physical reactions and not necessarily with all cases of MaxEnt subject to the constraints ((2)).</p> <p> In particular, we argue that the Tsallis type of distribution also follows from MaxEnt with ((2)), but does not allow for ((1)). This might mean that one does not have a picture of colliding independent particles forming the equilibrium. We thus suggest MaxEnt is more general than the physical independent two particle collision picture which makes sense for an ideal gas, but might not cover all physical situations (i.e. a Tsallis case).</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20244405 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | MaxEnt Versus p(ei)p(ej) = p(ei+ej) Ruggeri, Francesco R. <p> The Maxwell-Boltzmann distribution is so closely linked to an ideal gas as well as to MaxEnt (maximum entropy subject to constraints) that one might associate properties of interactions in the gas with MaxEnt in general. We argue that MaxEnt solutions may exist which do not conform to the interactions of the ideal gas. In particular, we argue that for an ideal gas: p(ei)p(ej) = p(ei+ej) ((1)) for physical reasons and this relation automatically yields p(ei)=Cexp(-ei/T) or - Sum over i p(ei) ln(p(ei) for entropy. As a result, it might seem that maximum entropy subject to the constraints Sum over i p(ei)=1 and Sum over i ei p(ei) = Eave ((2)) is equivalent to ((1)). We argue here that this is only one case. Maximum entropy for the constraints ((2)) has two solutions, and only one corresponds to ((1)), namely F=ln(p) for entropy = - Sum over i p(ei) F(p(ei)). As a result, ln(p), the Maxwell-Boltzmann case of F is linked with one kind of maximization of entropy and certain physical reactions and not necessarily with all cases of MaxEnt subject to the constraints ((2)).</p> <p> In particular, we argue that the Tsallis type of distribution also follows from MaxEnt with ((2)), but does not allow for ((1)). This might mean that one does not have a picture of colliding independent particles forming the equilibrium. We thus suggest MaxEnt is more general than the physical independent two particle collision picture which makes sense for an ideal gas, but might not cover all physical situations (i.e. a Tsallis case).</p> <p> </p> |
| title | MaxEnt Versus p(ei)p(ej) = p(ei+ej) |
| url | https://doi.org/10.5281/zenodo.20244405 |