This paper develops a philosophical investigation of the merits and faults of a theorem by Lanford , Lanford , Lanford for the problem of the approach towards equilibrium in statistical mechanics. Lanford’s result shows that, under precise initial conditions, the Boltzmann equation can be rigorously derived from the Hamiltonian equations of motion for a hard spheres gas in the Boltzmann-Grad limit, thereby proving the existence of a unique solution of the Boltzmann equation, at least for a very short amount of time. We argue that, by establishing a statistical H-theorem, it offers a prospect to complete Boltzmann’s combinatorial argument, without running against the objections which plug other typicality-based approaches. However, we submit that, while recovering the irreversible approach towards equilibrium for positive times, it fails to predict a monotonic increase of entropy for negative times, and hence it yields the wrong retrodictions about the past evolution of a gas
Keywords Approach to equilibrium   Statistical mechanics   Boltzmann
Categories (categorize this paper)
DOI 10.1007/s13194-014-0086-5
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 55,968
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The “Past Hypothesis”: Not Even False.John Earman - 2006 - Studies in History and Philosophy of Modern Physics 37 (3):399-430.
The Oxford Handbook of Philosophy of Physics.Robert W. Batterman (ed.) - 2013 - Oxford University Press USA.

View all 7 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Boltzmann, Gibbs, and the Concept of Equilibrium.David Lavis - 2008 - Philosophy of Science 75 (5):682-696.
The Coarse-Graining Approach to Statistical Mechanics: How Blissful is Our Ignorance?Katinka Ridderbos - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (1):65-77.
Thermal Equilibrium Between Radiation and Matter.G. Lanyi - 2003 - Foundations of Physics 33 (3):511-528.
Foundations of Statistical Mechanics—Two Approaches.Stephen Leeds - 2003 - Philosophy of Science 70 (1):126-144.
A Probabilistic Foundation of Elementary Particle Statistics. Part I.Domenico Costantini & Ubaldo Garibaldi - 1997 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (4):483-506.


Added to PP index

Total views
15 ( #643,805 of 2,403,324 )

Recent downloads (6 months)
1 ( #551,892 of 2,403,324 )

How can I increase my downloads?


My notes