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

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. In our previous study [Z.-Y. Yang and J.-X. Hou, Phys. Rev. E 101, 052106 (2020)10.1103/PhysRevE.101.052106], we observed the non-Markovian Mpemba effect in a mean-field system (MFS), where the Mpemba effect originates from the back-reaction of the thermal reservoir. Naturally, the phase transition time is the key to the occurrence of the Mpemba effect, which, however, has not been quantitatively described. Following the direction of previous work, this study rigorously derives the phase transition time under different conditions, and quantitatively describes the mechanism of the non-Markovian Mpemba effect in a MFS. In addition, the validation of our theory was further verified via the microcanonical Monte Carlo simulation. An accurate description of the underlying mechanism of our proposed MFS facilitates the generalization of the Mpemba effect framework in statistical physics and may benefit in answering the riddle of the century, the original Mpemba effect in water.

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. Moreover, the global phase diagram of this model is given in both ensembles.

Non-Clausius heat transfer: The method of the nonstationary Langevin equation

Compared to other formulations of the second law of thermodynamics, the Clausius statement that heat does not spontaneously flow from cold to hot concerns a system in nonequilibrium states, and in that respect is more ambitious but also more ambiguous. We discuss two scenarios when the Clausius statement in its plain form does not hold. First, for ergodic systems, the energy transfer may be consistent with the statement on a coarse-grained timescale, but be anomalously directed during time intervals shorter than the thermalization time. In particular, when an initially colder system is brought in contact to a hotter bath, the internal energy of the former increases with time in a long run but not monotonically. Second, the heat transfer may not respect the Clausius statement on any timescale in nonergodic systems due to the formation of localized vibrational modes. We illustrate the two scenarios with a familiar model of an isotope atom attached to a semi-infinite harmonic atomic chain. Technically, the discussion is based on a Langevin equation for the isotope, using the initial condition when the isotope and chain are initially prepared in uncorrelated canonical states under the constraint that the boundary atom between the isotope and chain is initially fixed and later released. In such setting, the noise in the Langevin equation is nonstationary, and the fluctuation-dissipation relation has a nonstandard form.

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. The simulation results unambiguously demonstrate that an initial hotter system undergoes the paramagnetic-ferromagnetic phase transition faster than the initial cooler one. The ME here originates from the back-reaction of the MFS system on the reservoir, which is thus an embodiment of non-Markovianness in relaxation. In addition, we confirm that the ME survives in the thermodynamic limit. And the significance of reservoir size is also explored: A smaller heat reservoir facilitates the overall relaxation process. In general, this work establishes a theoretical non-Markovian ME framework, which may shed light on widening the understanding of the mechanism behind the ME in other substances, including water.