sharma-mittal-entropy-gravity

name	sharma-mittal-entropy-gravity
description	Sharma-Mittal entropy framework bridging information theory, black hole thermodynamics, and infrared gravity modifications. Derives modified gravitational force laws from generalized entropy, reproduces MOND-like regime. Activates: sharma-mittal entropy, generalized entropy, emergent gravity, MOND, black hole thermodynamics, information bounds, infrared gravity, entropic gravity
metadata	{"arxiv_id":"2606.15996","published":"2026-06-14","authors":"Abdelhakim Benkrane, Giuseppe Gaetano Luciano, Ahmad Sheykhi","tags":["information-theory","gravity","thermodynamics","black-hole","MOND","emergent-gravity"]}

Sharma-Mittal Entropy Framework for Gravity

Description

Sharma-Mittal (SM) entropy provides a two-parameter generalization encompassing both Renyi and Tsallis frameworks. This methodology connects generalized entropy to gravitational physics through black hole thermodynamics and entropic gravity.

Activation Keywords

• sharma-mittal entropy
• generalized entropy gravity
• emergent gravity MOND
• black hole thermodynamics
• entropic gravity modified
• information bounds gravity
• infrared gravity modification

Core Methodology

Framework Components

1. Sharma-Mittal Entropy: Two-parameter (R, delta) generalization that interpolates between Renyi and Tsallis entropies in appropriate limits

2. Bekenstein Bound Compatibility: Gravitational realization of SM entropy consistently interpolates between Renyi and Bekenstein-Hawking entropies

3. Landauer's Principle Extension: Modified mass-loss relation from one-bit information erasure with parameter-dependent asymptotic behavior in small- and large-mass regimes

4. Entropic Gravity Modification: Within Verlinde's entropic gravity framework, derive modified gravitational force and acceleration laws induced by SM entropy

Key Results

• Modified acceleration deviates from Newtonian prediction at large distances
• Naturally reproduces MOND-like regime for parameter relation R/delta = 3/2
• Direct connection between SM entropy parameters and MOND acceleration scale a_0
• Links black hole thermodynamics, information theory, and infrared gravity modifications

Usage Patterns

Pattern 1: Entropic Gravity Derivation

When studying how generalized entropy frameworks modify gravitational laws:

1. Define the generalized entropy function S_SM(m, R, delta)
2. Apply Landauer's principle: delta M = T delta S
3. Derive modified mass-loss/acceleration relations
4. Compare with Newtonian prediction at various distance scales
5. Identify parameter regimes reproducing observed phenomena (e.g., MOND)

Pattern 2: Black Hole Thermodynamics Analysis

When analyzing black hole entropy with generalized statistical frameworks:

1. Check compatibility with Bekenstein bound
2. Compute entropy in appropriate limits (R -> 0, delta -> 0)
3. Verify interpolation between known entropy forms
4. Study asymptotic behavior in small/large mass regimes

Pattern 3: Information-Gravity Connection

When exploring how information-theoretic quantities manifest in gravitational physics:

1. Identify the information-theoretic measure (entropy, mutual information)
2. Map to thermodynamic quantities via Landauer/Verlinde frameworks
3. Derive gravitational consequences
4. Test against observational constraints

Related Skills

• quantum-information-science - broader information theory context
• quantum-fisher-information-duality - QFI as information-theoretic measure
• quantum-metabolic-neuroimaging-limit - fundamental information bounds