The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics
The long-standing and highly non-trivial problem of calculating the pressure fluctuations in the Gibbs equilibrium statistical mechanics is fully revised. The previous attempts are critically analyzed and it is shown that the application of the ideas by Bogolyubov gives the full and unambiguous solu...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute for Condensed Matter Physics
2009-01-01
|
| Series: | Condensed Matter Physics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.5488/CMP.12.4.581 |
| _version_ | 1828404133045993472 |
|---|---|
| author | Yu.G. Rudoy |
| author_facet | Yu.G. Rudoy |
| author_sort | Yu.G. Rudoy |
| collection | DOAJ |
| description | The long-standing and highly non-trivial problem of calculating the pressure fluctuations in the Gibbs equilibrium statistical mechanics is fully revised. The previous attempts are critically analyzed and it is shown that the application of the ideas by Bogolyubov gives the full and unambiguous solution of this problem. The crucial role is played by the Bogolyubov's idea of quasiaverages (or rather quasidynamic) quantities - specifically, the pressure P and dynamic compressibility Ψ. The virtual conjugate field which eliminates the translational invariance of the Hamilton function H in the limit ε→ 0 is the singular potential of the impenetrable walls of the container. The general relations for P and Ψ in terms of the derivatives of H are obtained and some examples are studied - i. e., the cases of the ideal vs. non-ideal as well as of uniform vs. non- and quasi-uniform (in Euler sense) Hamilton function H describing the given system. |
| first_indexed | 2024-12-10T10:31:14Z |
| format | Article |
| id | doaj.art-89ed2ec9e74e47589c5e04a53d5c25ec |
| institution | Directory Open Access Journal |
| issn | 1607-324X |
| language | English |
| last_indexed | 2024-12-10T10:31:14Z |
| publishDate | 2009-01-01 |
| publisher | Institute for Condensed Matter Physics |
| record_format | Article |
| series | Condensed Matter Physics |
| spelling | doaj.art-89ed2ec9e74e47589c5e04a53d5c25ec2022-12-22T01:52:34ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2009-01-01124581592The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanicsYu.G. RudoyThe long-standing and highly non-trivial problem of calculating the pressure fluctuations in the Gibbs equilibrium statistical mechanics is fully revised. The previous attempts are critically analyzed and it is shown that the application of the ideas by Bogolyubov gives the full and unambiguous solution of this problem. The crucial role is played by the Bogolyubov's idea of quasiaverages (or rather quasidynamic) quantities - specifically, the pressure P and dynamic compressibility Ψ. The virtual conjugate field which eliminates the translational invariance of the Hamilton function H in the limit ε→ 0 is the singular potential of the impenetrable walls of the container. The general relations for P and Ψ in terms of the derivatives of H are obtained and some examples are studied - i. e., the cases of the ideal vs. non-ideal as well as of uniform vs. non- and quasi-uniform (in Euler sense) Hamilton function H describing the given system.http://dx.doi.org/10.5488/CMP.12.4.581Gibbs equilibrium statistical mechanicsBogolyubov's quasiaveragespressure fluctuationsrelativistic ideal gas |
| spellingShingle | Yu.G. Rudoy The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics Condensed Matter Physics Gibbs equilibrium statistical mechanics Bogolyubov's quasiaverages pressure fluctuations relativistic ideal gas |
| title | The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics |
| title_full | The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics |
| title_fullStr | The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics |
| title_full_unstemmed | The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics |
| title_short | The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics |
| title_sort | bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the gibbs statistical mechanics |
| topic | Gibbs equilibrium statistical mechanics Bogolyubov's quasiaverages pressure fluctuations relativistic ideal gas |
| url | http://dx.doi.org/10.5488/CMP.12.4.581 |
| work_keys_str_mv | AT yugrudoy thebogolyubovmethodofquasiaveragessolvestheproblemofpressurefluctuationsinthegibbsstatisticalmechanics AT yugrudoy bogolyubovmethodofquasiaveragessolvestheproblemofpressurefluctuationsinthegibbsstatisticalmechanics |