Landau Theory for the Mpemba Effect Through Phase Transitions

Abstract

The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.

11 pages, 6 figures

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• Anomalous heating in a colloidal system
• Should a hotter paramagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model
• Mpemba effect in inertial suspensions
• The metastable Mpemba effect corresponds to a non-monotonic temperature dependence of extractable work
• Finite-time dynamical phase transition in non-equilibrium relaxation
• Mpemba effect in an anisotropically driven granular gas
• Anomalous thermal relaxation of Langevin particles in a piecewise-constant potential
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• Quantum Mpemba effect in a quantum dot with reservoirs
• Multiple quantum Mpemba effect: exceptional points and oscillations
• The quantum Mpemba effects
• Mpemba effects in open nonequilibrium quantum systems
• Relaxation shortcuts through boundary coupling
• Eigenvalue crossing as a phase transition in relaxation dynamics
• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects
• Quantum Mpemba Effects from Symmetry Perspectives
• Mpemba effect in a Langevin system: population statistics, metastability and other exact results
• Nonequilibrium Phase Transition To Temporal Oscillations In Mean-Field Spin Models
• Landau theory for finite-time dynamical phase transitions
• Quantum Mpemba effect without global symmetries
• Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law
• Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model
• Non-equilibrium memory effects: granular fluids and beyond
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Imaginary-time Mpemba effect in quantum many-body systems
• Critical Fluctuations at Finite-Time Dynamical Phase Transition
• Mpemba effect in the relaxation of an active Brownian particle in a trap without metastable states
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Mpemba effect on non-equilibrium active Markov chains
• Thermographic study of freezing water drops: An insight on Mpemba effect