On the entropic derivation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> Newtonian gravity force

Plastino, A.; Rocca, Mario Carlos

doi:10.1016/j.physa.2018.03.037

Cited by 23 publications

(36 citation statements)

References 25 publications

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“…This expression is plotted in Figure 2. We see that the specific heat is always positive, as it happens in the non-relativistic case [8].…”

Section: Specific Heat In the Linear Constraints Tsallis' Scenariomentioning

confidence: 54%

“…We consider first the case q < 1. This case is not relevant to our Verlinde's endeavor [8], but is a logical addition to the results of [6].…”

Section: Tsallis' Relativistic Partition Function For the Free Particlementioning

confidence: 80%

“…Let is now calculate the specific heat for the case q = 4 3 , relevant for Verlindeendeavors [8]. This was not done in [6].…”

Section: Specific Heat In the Linear Constraints Tsallis' Scenariomentioning

confidence: 99%

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Relativistic treatment of Verlinde’s emergent force in Tsallis’ statistics

et al. 2019

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Following Chakrabarti,Chandrasekhar, and Naina [Physica A 389 (2010) 1571], we attempt a classical relativistic treatment of Verlinde's emergent entropic force conjecture by appealing to a relativistic Hamiltonian in the context of Tsalli's statistics. The ensuing partition function becomes the classical one for small velocities. We show that Tsallis' relativistic (classical) free particle distribution at temperature T can generate Newton's gravitational force's r −2 distance's dependence. If we want to repeat the concomitant argument by appealing to Renyi's distribution, the attempt fails and one needs to modify the conjecture.

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“…This expression is plotted in Figure 2. We see that the specific heat is always positive, as it happens in the non-relativistic case [8].…”

Section: Specific Heat In the Linear Constraints Tsallis' Scenariomentioning

confidence: 54%

“…We consider first the case q < 1. This case is not relevant to our Verlinde's endeavor [8], but is a logical addition to the results of [6].…”

Section: Tsallis' Relativistic Partition Function For the Free Particlementioning

confidence: 80%

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Relativistic treatment of Verlinde’s emergent force in Tsallis’ statistics

et al. 2019

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“…1 we plot F e with m= uranium's atom mass. E = N mv 2 2 , v = 1000 meter/second, and N = 500 yielding r 3 > 1.525 × 10 −33 The cut-off originates because F e takes now the simplified form We have considered, for fermions, Verlinde's [entropic force -Gravitation] link, proved recently both in a classical context [2] and in a quantum bosonic scenario [3]. We have seen that Verlinde's conjecture holds also for a Fermi environment.…”

Section: Resultsmentioning

confidence: 99%

“…Eight years ago, Verlinde [1] proposed to establish a bridge linking gravity with an entropic force. The ensuing conjecture was proved recently I) in a purely classical environment [2] and II) in [3] for the Bose-Einstein statistics.…”

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confidence: 92%

Spatial cut-offs, Fermion statistics, and Verlinde’s conjecture

Plastino

Rocca

2019

Physica A: Statistical Mechanics and its Applications

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Verlinde conjectured eight years ago that gravitation might be an emergent entropic force. This rather surprising assertion was proved in [Physica A 505 (2018) 190] within a purely classical statistical context, and in [] for the case of bosons' statistics. In the present work, we appeal to a quantum scenario involving fermions' statistics. We consider also the classical limit of quantum (statistical) mechanics (QM). We encounter a lower bound to the distance r between the two interacting masses, i.e., an r cut-off. This is a new effect that exhibits some resemblance with the idea of space discretization proposed by recent gravitation theories.

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