Microscopic Theory of Phase Transitions in Freeway Traffic

2004 ◽  
pp. 433-448
Author(s):  
Boris S. Kerner
Keyword(s):  
Phase Transitions ◽  
Microscopic Theory ◽  
Freeway Traffic

scholarly journals Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
A. I. Sokolovsky
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
General Formula ◽  
Correlation Functions ◽  
Nonequilibrium Thermodynamic ◽  
Microscopic Theory ◽  
Effective Hamiltonian ◽  
Equilibrium Fluctuations ◽  
Thermodynamic Potentials ◽  
Definition Of

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed. In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered. A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

scholarly journals Microscopic theory of magnetic phase transitions inHoNi2B2C

1998 ◽  
Vol 57 (17) ◽  
pp. 10684-10687 ◽  
Author(s):  
A. Amici ◽  
P. Thalmeier
Keyword(s):  
Phase Transitions ◽  
Magnetic Phase ◽  
Microscopic Theory ◽  
Magnetic Phase Transitions

ANOMALOUS DIFFUSION NEAR STRUCTURAL PHASE TRANSITIONS

1992 ◽  
Vol 06 (18) ◽  
pp. 1099-1103 ◽  
Author(s):  
W. K. HAN ◽  
S. C. YING ◽  
T. ALA-NISSILA
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Inhomogeneous Medium ◽  
Anomalous Diffusion ◽  
Structural Phase ◽  
Microscopic Theory ◽  
Central Peak ◽  
Structural Phase Transitions ◽  
Model Calculations ◽  
Physical Systems

Using a recently developed microscopic theory of diffusion for a particle coupled to an inhomogeneous medium, it has been shown that in the case of a structural phase transition with a diverging central peak, a diffusion anomaly occurs. We review results of model calculations demonstrating this anomaly on the W(100) surface, as well as discuss other physical systems where analogous phenomena may be observed.

scholarly journals Microscopic theory of phase transitions in a critical region

2015 ◽  
Vol 90 (10) ◽  
pp. 108002 ◽  
Author(s):  
Vitaly V Kocharovsky ◽  
Vladimir V Kocharovsky
Keyword(s):  
Phase Transitions ◽  
Critical Region ◽  
Microscopic Theory
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