The thermodynamic limit and the limit Gibbs distribution

1999 ◽  
pp. 21-24
Author(s):  
R. Minlos
Keyword(s):  
Thermodynamic Limit ◽  
Gibbs Distribution

What good is the thermodynamic limit?

2004 ◽  
Vol 72 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Daniel F. Styer
Keyword(s):  
Thermodynamic Limit

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

METASTABLE STATES IN THE HOPFIELD MODEL

1990 ◽  
Vol 04 (01) ◽  
pp. 143-150 ◽  
Author(s):  
CLAUDIO PROCESI ◽  
BRUNELLO TIROZZI
Keyword(s):  
Free Energy ◽  
Finite Number ◽  
Thermodynamic Limit ◽  
Metastable States ◽  
Hopfield Model ◽  
Zero Temperature

We describe the properties of the free energy of the Hopfield model with a finite number of patterns and describe its dynamic at zero temperature in the space of overlaps in the thermodynamic limit.

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