Brownian particles with long- and short-range interactions

Physica A: Statistical Mechanics and its Applications

Volumn 390, Issue 9, 2011, Pages 1546-1574

  Chavanis, Pierre Henri ^a  

^a UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

Brownian particles; Generalized thermodynamics; Kinetic theory; Long range interactions; Nonlinear mean field FokkerPlanck equations

Indexed keywords

BIOCHEMISTRY; BROWNIAN MOVEMENT; COLLOIDS; FOKKER PLANCK EQUATION; FREE ENERGY; HYDRODYNAMICS; KINETIC THEORY; KINETICS; PROBABILITY DISTRIBUTIONS; SUSPENSIONS (FLUIDS);

ATTRACTIVE INTERACTIONS; BROWNIAN PARTICLES; CAPILLARY INTERACTIONS; HYDRODYNAMIC EQUATIONS; LONG RANGE INTERACTIONS; SHORT RANGE INTERACTIONS; SMOLUCHOWSKI-POISSON SYSTEM; TRANSITION PROBABILITIES;

NONLINEAR EQUATIONS;

EID: 79952105141     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2010.12.018     Document Type: Article

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78. The non-commutation of the limits t → + ∞ and N → + ∞ that we discuss here is different from the one reported by Latora et al. [81] in relation to quasi stationary states (QSSs). These authors consider isolated Hamiltonian systems with long-range interactions, in the absence of metastable states, and discuss the difference between QSSs (steady states of the Vlasov equation [82]) obtained when the N → + ∞ limit is taken before the t → + ∞ limit and statistical equilibrium states (global entropy maxima) obtained when the t → + ∞ limit is taken before the N → + ∞ limit. Here, we consider overdamped Brownian systems with long-range interactions and discuss the difference between metastable states (local free energy minima) obtained when the N → + ∞ limit is taken before the t → + ∞ limit and strict statistical equilibrium states (global free energy minima) obtained when the t → + ∞ limit is taken before the N → + ∞ limit. A more detailed discussion is provided in Appendix C.
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