Theoretical model for the Mpemba effect through the canonical first-order phase transition.

The Mpemba effect is the phenomenon in which the system with high initial temperature cools faster than the system with low initial temperature when all other conditions are the same. A theoretical model of the Mpemba effect through the canonical first-order phase transition is proposed in this paper, which shows that in the cooling processes, the path of the first-order phase transition of the system with the high initial temperature does not pass through any metastable state, while the path of the first-order phase transition of the system with the low initial temperature passes through a metastable state, which leads to the occurrence of the Mpemba effect. Then an example of the theoretical model is given in the Blume-Emery-Griffiths model.

Mpemba effect of a mean-field system: The phase transition time.

The counterintuitive phenomenon-that an initially hotter water freezes faster than initially cooler water-is named the "Mpemba effect." Although it has been known for centuries, the underlying mechanism remains unclear. Recently, the Mpemba effect rekindled the interest of researchers since several studies identified that it might occur in some Markovian systems, and a general statistical-physical Mpemba effect framework was correspondingly proposed.

Zeroth-order phase transition in the Blume-Emery-Griffiths model without bilinear exchange coupling.

We study the simplified Blume-Emery-Griffiths model without bilinear exchange coupling both in the microcanonical ensemble and in the canonical ensemble. This model can exhibit a zeroth-order phase transition in the microcanonical ensemble accompanied by a finite entropy jump. However, this singularity in entropy cannot be observed in the canonical ensemble, which illustrates the ensemble inequivalence.

Comment on "Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions".

In a recent paper by Fronczak et al. [Phys. Rev.

Non-Markovian Mpemba effect in mean-field systems.

Under certain conditions, a counterintuitive behavior-an initially hotter sample freezes faster when quenched to a cold bath than an identical system initialled at a lower temperature-is known as the Mpemba effect (ME). Here we identify the existence of the ME in mean-field systems (MFS). Specifically, the thermal contact between MFS and a large thermal reservoir is built up using the microcanonical Monte Carlo algorithm.

Determine Mesh Size through Monomer Mean-Square Displacement.

A dynamic method to determine the main parameter of the tube theory through monomer mean-square displacement is discussed in this paper. The tube step length can be measured from the intersection of the slope- 1 2 line and the slope- 1 4 line in log-log plot, and the tube diameter can be obtained by recording the time at which g 1 data start to leave the slope- 1 2 regime. According to recent simulation data, the ratio of the tube step length to the tube diameter was found to be about 2 for different entangled polymer systems.

Violation of the temperature-signifies-heat-flow rule in systems with long-range interactions.

For a long-range interacting spin chain model, the microcanonical ensemble predicts a region of negative specific heat and a temperature jump at the transition energy. After two similar long-range interacting subsystems of different size at different temperatures are weakly coupled, they exchange energy and the total microcanonical entropy of the full system increases irreversibly. The hot subsystem could spontaneously absorb heat from the cold subsystem via the thermal contact and the final equilibrium temperature could be lower than the initial temperatures of the cold subsystem.

Note: Determine entanglement length through monomer mean-square displacement.

I present a refined version of the method for determining entanglement length through monomer mean-square displacement. By retrieving a prefactor π/2 that might be lost in previous derivation, the entanglement length of the standard bead-spring model estimated by this method coincides with the measurements of other methods.

Stress relaxation in entangled polymer melts.

We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements and into the terminal relaxation regime for Z=10. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter-free tests of several different tube models.