Difference between revisions of "Thermodynamical limit"
From Encyclopedia of Mathematics
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| − | A fundamental method in statistical physics, consisting of the study of a large (but finite) physical system by approximating it by some infinite idealized system. For example, a system consisting of | + | {{TEX|done}} |
| + | A fundamental method in statistical physics, consisting of the study of a large (but finite) physical system by approximating it by some infinite idealized system. For example, a system consisting of $N$ particles (molecules) filling out a bounded domain $\Lambda$ in $\mathbb{R}^3$ can be replaced, for large $N$ and a large domain $\Lambda$ (compared to the size of a molecule), by a system of infinitely many such molecules filling out the whole space, in such a way that the properties and characteristics of the finite system (the dynamical character, the equilibrium property of ensembles, etc.) are close to the analogous properties and characteristics of the limit system. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> D. Ruelle, "Statistical mechanics: rigorous results" , Benjamin (1974)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> , ''Gibbs states in statistical physics'' , Moscow (1978) (In Russian; translated from English)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> R.A. Minlos, "Lectures on statistical physics" ''Russian Math. Surveys'' , '''23''' : 1 (1968) pp. 137–196 ''Uspekhi Mat. Nauk'' , '''23''' : 1 (1968) pp. 133–190</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> D. Ruelle, "Statistical mechanics: rigorous results" , Benjamin (1974)</TD></TR> | ||
| + | <TR><TD valign="top">[2]</TD> <TD valign="top"> , ''Gibbs states in statistical physics'' , Moscow (1978) (In Russian; translated from English)</TD></TR> | ||
| + | <TR><TD valign="top">[3]</TD> <TD valign="top"> R.A. Minlos, "Lectures on statistical physics" ''Russian Math. Surveys'' , '''23''' : 1 (1968) pp. 137–196 ''Uspekhi Mat. Nauk'' , '''23''' : 1 (1968) pp. 133–190</TD></TR> | ||
| + | </table> | ||
| Line 10: | Line 15: | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J.W. Gibbs, "Elementary principles in statistical mechanics" , Dover, reprint (1960)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> L.D. Landau, E.M. Lifshitz, "Statistical physics" , Pergamon (1980) (Translated from Russian)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> D. Ruelle, "Thermodynamic formalism" , Addison-Wesley (1978)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> J.W. Gibbs, "Elementary principles in statistical mechanics" , Dover, reprint (1960)</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> L.D. Landau, E.M. Lifshitz, "Statistical physics" , Pergamon (1980) (Translated from Russian)</TD></TR> | ||
| + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> D. Ruelle, "Thermodynamic formalism" , Addison-Wesley (1978) {{ZBL|0401.28016}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 20:32, 28 December 2014
A fundamental method in statistical physics, consisting of the study of a large (but finite) physical system by approximating it by some infinite idealized system. For example, a system consisting of $N$ particles (molecules) filling out a bounded domain $\Lambda$ in $\mathbb{R}^3$ can be replaced, for large $N$ and a large domain $\Lambda$ (compared to the size of a molecule), by a system of infinitely many such molecules filling out the whole space, in such a way that the properties and characteristics of the finite system (the dynamical character, the equilibrium property of ensembles, etc.) are close to the analogous properties and characteristics of the limit system.
References
| [1] | D. Ruelle, "Statistical mechanics: rigorous results" , Benjamin (1974) |
| [2] | , Gibbs states in statistical physics , Moscow (1978) (In Russian; translated from English) |
| [3] | R.A. Minlos, "Lectures on statistical physics" Russian Math. Surveys , 23 : 1 (1968) pp. 137–196 Uspekhi Mat. Nauk , 23 : 1 (1968) pp. 133–190 |
Comments
References
| [a1] | J.W. Gibbs, "Elementary principles in statistical mechanics" , Dover, reprint (1960) |
| [a2] | L.D. Landau, E.M. Lifshitz, "Statistical physics" , Pergamon (1980) (Translated from Russian) |
| [a3] | D. Ruelle, "Thermodynamic formalism" , Addison-Wesley (1978) Zbl 0401.28016 |
How to Cite This Entry:
Thermodynamical limit. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Thermodynamical_limit&oldid=18793
Thermodynamical limit. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Thermodynamical_limit&oldid=18793
This article was adapted from an original article by R.A. Minlos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article