Tolman-Ehrenfest-Klein Law in non-Riemannian geometries

Abstract

Heat always flows from hotter to a colder temperature until thermal equilibrium be finally restored in agreement with the usual (zeroth, first and second) laws of thermodynamics. However, Tolman and Ehrenfest demonstrated that the relation between inertia and weight uniting all forms of energy in the framework of general relativity implies that the standard equilibrium condition is violated in order to maintain the validity of the first and second law of thermodynamics. Here we demonstrate that the thermal equilibrium condition for a static self-gravitating fluid, besides being violated, is also heavily dependent on the underlying spacetime geometry (whether Riemannian or non-Riemannian). As a particular example, a new equilibrium condition is deduced for a large class of Weyl and f(R) type gravity theories. Such results suggest that experiments based on the foundations of the heat theory (thermal sector) may also be used for confronting gravity theories and prospect the intrinsic geometric nature of the spacetime structure.

arXiv comment5 pages, no figures. Accepted for publication in Physical Review D

References in corpus (15)

• f(R) Theories Of Gravity
• Extended Theories of Gravity
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Metric-affine f(R) theories of gravity
• Local Conformal Symmetry in Physics and Cosmology
• Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
• General Relativity and Weyl Geometry
• Gauging scale symmetry and inflation: Weyl versus Palatini gravity
• Thermodynamical instabilities of perfect fluid spheres in General Relativity
• Temperature Evolution Law of Imperfect Relativistic Fluids
• Tolman-like temperature gradients in stationary spacetimes
• Local conformal symmetry in non-Riemannian geometry and the origin of physical scales
• Thermodynamic Equilibrium in General Relativity
• Unruh versus Tolman: On the heat of acceleration
• Is Asymptotically Weyl-Invariant Gravity Viable?

Cited by in corpus (3)

• Tolman-Ehrenfest's criterion of thermal equilibrium extended to conformally static spacetimes
• How the Schwarzschild-de Sitter horizons remain in thermal equilibrium at vastly different temperatures
• Thermodynamic parameters of fluids on conformally connected spacetimes