Phase Transitions in "Small" Systems - A Challenge for Thermodynamics

Details Phase Transitions in "Small" Systems - A Challenge for Thermodynamics Phase Transitions in "Small" Systems - A Challenge for Thermodynamics

2000-06-06

arxiv.org/abs/cond-mat/0006087v1

Nucl.Phys. A681 (2001) 366-373

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures, Invited paper for CRIS2000

Scientific paper

10.1016/S0375-9474(00)00540-6

Traditionally, phase transitions are defined in the thermodynamic limit only. We propose a new formulation of equilibrium thermo-dynamics that is based entirely on mechanics and reflects just the {\em geometry and topology} of the N-body phase-space as function of the conserved quantities, energy, particle number and others. This allows to define thermo-statistics {\em without the use of the thermodynamic limit}, to apply it to ``Small'' systems as well and to define phase transitions unambiguously also there. ``Small'' systems are systems where the linear dimension is of the characteristic range of the interaction between the particles. Also astrophysical systems are ``Small'' in this sense. Boltzmann defines the entropy as the logarithm of the area $W(E,N)=e^{S(E,N)}$ of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant $D(E,N)=\partial^2S/\partial E^2*\partial^2S/\partial N^2-(\partial^2S/\partial E\partial N)^2$ allows the classification of phase transitions {\em without taking the thermodynamic limit}. The topology gives further a simple and transparent definition of the {\em order parameter.} Attention: Boltzmann's entropy S(E) as defined here is different from the information entropy and can even be non-extensive and convex.

Affiliated with

Also associated with

No associations

Rating

Phase Transitions in "Small" Systems - A Challenge for Thermodynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Phase Transitions in "Small" Systems - A Challenge for Thermodynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase Transitions in "Small" Systems - A Challenge for Thermodynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-482365