Boltzmann's $H$-theorem, entropy and the strength of gravity in theories with a nonminimal coupling between matter and geometry

Abstract

In this paper we demonstrate that Boltzmann's $H$-theorem does not necessarily hold in the context of theories of gravity with nonminimally coupled matter fields. We find sufficient conditions for the violation of Boltzmann's $H$-theorem and derive an expression for the evolution of Boltzmann's $H$ in terms of the nonminimal coupling function, valid in the case of a collisionless gas in a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker universe. We highlight the implications of this result for the evolution of the entropy of the matter fields, briefly discussing the role played by collisions between particles whenever they are relevant. We also suggest a possible link between the high entropy of the Universe and the weakness of gravity in the context of these theories.

7 pages, no figures. Clarifications added, typos corrected. Results unchanged

References in corpus (10)

• The Confrontation between General Relativity and Experiment
• f(R,T) gravity
• Extra force in $f(R)$ modified theories of gravity
• f(R,L_m) gravity
• Nonminimal coupling of perfect fluids to curvature
• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• A viability criterion for modified gravity with an extra force
• Extended $f(R,L_m)$ gravity with generalized scalar field and kinetic term dependences
• Probing gravity at sub-femtometer scales through the pressure distribution inside the proton
• Particle creation and decay in nonminimally coupled models of gravity

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• Modified Gravity with Nonminimal Curvature-Matter Couplings: A Framework for Gravitationally Induced Particle Creation
• Lagrangian Identity and Mass Evolution of Particle-like Objects in Nonminimally Coupled Gravity