Next Article in Journal
Real-Time Robust Voice Activity Detection Using the Upper Envelope Weighted Entropy Measure and the Dual-Rate Adaptive Nonlinear Filter
Next Article in Special Issue
Entropy Measures as Geometrical Tools in the Study of Cosmology
Previous Article in Journal
A Kernel-Based Intuitionistic Fuzzy C-Means Clustering Using a DNA Genetic Algorithm for Magnetic Resonance Image Segmentation
Previous Article in Special Issue
Statistics of Binary Exchange of Energy or Money
Article Menu
Issue 11 (November) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(11), 537;

Gravitational Contribution to the Heat Flux in a Simple Dilute Fluid: An Approach Based on General Relativistic Kinetic Theory to First Order in the Gradients

Departamento de Fisica y Matematicas, Universidad Iberoamericana Ciudad de Mexico, Prolongacion Paseo de la Reforma 880, Mexico D.F. 01219, Mexico
Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Prolongacion Vasco de Quiroga 4871, Mexico D.F. 05348, Mexico
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 11 August 2017 / Revised: 27 September 2017 / Accepted: 9 October 2017 / Published: 28 October 2017
(This article belongs to the Special Issue Advances in Relativistic Statistical Mechanics)
Full-Text   |   PDF [243 KB, uploaded 28 October 2017]


Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman’s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by explicitly describing the single particle orbits as geodesics in Boltzmann’s equation, that a gravitational field drives a heat flux in this type of system. The calculation is devoted solely to the gravitational field contribution to this heat flux in which a Newtonian limit to the Schwarzschild metric is assumed. The corresponding transport coefficient, which is obtained within a relaxation approximation, corresponds to the dilute fluid in a weak gravitational field. The effect is negligible in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit. View Full-Text
Keywords: relativity; kinetic theory; fluid mechanics; heat conduction relativity; kinetic theory; fluid mechanics; heat conduction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Brun-Battistini, D.; Sandoval-Villalbazo, A.; Garcia-Perciante, A.L. Gravitational Contribution to the Heat Flux in a Simple Dilute Fluid: An Approach Based on General Relativistic Kinetic Theory to First Order in the Gradients. Entropy 2017, 19, 537.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top