Zheng: Phase Transition

Zitat

„Percolation transition, the transition from a disconnected state to a connected one, has been regarded as a fundamental model of phase transitions in nonequilibrium systems. One of the most fundamental characteristics of a phase transition is its order, i.e., whether the macroscopic quantity affects changes continuously or discontinuously at the transition point. The percolation phase transitions in random networks were originally considered to be robust continuous phase transitions.“ (p. vii) #Zheng #percolation #PhaseTransition #random #network

Zheng, Zhiming, Supervisor’s Foreword, in: Explosive Percolation in Random Networks. Berlin/Heidelberg: Springer 2014, vii–viii.

Chen: Phase Transition

Zitat

„One of the most fundamental characteristics of a phase transition is its order, i.e., whether the macroscopic quantity it affects changes continuously or discontinuously at the transition point. Continuous transitions are called ’second-order‘ and include many magnetization phenomena, whereas discontinuous transitions are called ‚first-order,‘ an example of which is the discontinuous drop in entropy when liquid water turns into solid ice at zero degrees.“ (p. 3) #Chen #PhaseTransition

Chen, Wei, Explosive Percolation in Random Networks. Berlin/Heidelberg: Springer 2014. 63 S.

Ruelle: Phase Transition

Zitat

„The main physical problem which equilibrium statistical mechanics tries to clarify is that of phase transitions. When the temperature of water is lowered, why do its properties change first smoothly, then suddenly as the freezing point is reached?“ (p. 1) #Ruelle #PhaseTransition

Ruelle, David, Thermodynamic Formalism. The Mathematical Structures of Equilibrium. Statistical Mechanics. Cambridge, UK: Cambridge University Press 22004.