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.

arXiv comment7 pages, no figures. Clarifications added, typos corrected. Results unchanged

References in corpus (25)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• 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
• Forces inside hadrons: pressure, surface tension, mechanical radius, and all that
• Gravity assisted dark energy dominance and cosmic acceleration
• Nonminimal coupling of perfect fluids to curvature
• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• Energy Conditions and Stability in $f(R)$ theories of gravity with non-minimal coupling to matter
• Modified gravity with R-matter couplings and (non-)geodesic motion
• Gravitational induced particle production through a nonminimal curvature-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
• A Gravitational Entropy Proposal
• Induced gravity with a non-minimally coupled scalar field on the brane
• QCD uncertainties at the LHC and the implications of HERA
• Perfect fluid Lagrangian and its cosmological implications in theories of gravity with nonminimally coupled matter fields
• Matter Lagrangian of particles and fluids
• Structure Formation and Backreaction in Growing Neutrino Quintessence
• Gravitational entropies in LTB dust models
• Big-bang nucleosynthesis and cosmic microwave background constraints on non-minimally coupled theories of gravity
• Probing gravity at sub-femtometer scales through the pressure distribution inside the proton
• Particle creation and decay in nonminimally coupled models of gravity

Cited by in corpus (7)

• Lagrangian description of cosmic fluids: mapping dark energy into unified dark energy
• On-shell Lagrangian of an ideal gas
• Distance-duality in theories with a nonminimal coupling to gravity
• Second law of thermodynamics in nonminimally coupled gravity
• Thermodynamics of the Primordial Universe
• 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