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The Mpemba effect denotes an anomalous relaxation phenomenon where a system initially at a hot temperature cools faster than a system that starts at a less elevated temperature. We introduce an isothermal analog of this effect for a system…

Statistical Mechanics · Physics 2022-09-02 Julius Degünther , Udo Seifert

Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to…

Quantum thermometry provides a key capability for nanoscale devices and quantum technologies, but most existing strategies rely on probes initialized near equilibrium. This equilibrium paradigm imposes intrinsic limitations: sensitivity is…

Quantum Physics · Physics 2026-01-09 Pritam Chattopadhyay , Jonas F. G. Santos , Avijit Misra

The Mpemba effect is a counter-intuitive relaxation phenomenon, where a system prepared at a hot temperature cools down faster than an identical system initiated at a cold temperature when both are quenched to an even colder bath. Such…

Statistical Mechanics · Physics 2019-07-03 Israel Klich , Oren Raz , Ori Hirschberg , Marija Vucelja

We present an exactly solvable model of the Mpemba effect in an overdamped Langevin system confined in a two-dimensional radially symmetric bistable potential. The potential is constructed as a piecewise quadratic-logarithmic function that…

Statistical Mechanics · Physics 2026-04-02 Hisao Hayakawa , Satoshi Takada

Most of our intuition about the behavior of physical systems is shaped by observations at or near thermal equilibrium. However, even a thermal quench can lead to states far from thermal equilibrium, where counterintuitive, anomalous effects…

Statistical Mechanics · Physics 2025-12-11 Gianluca Teza , John Bechhoefer , Antonio Lasanta , Oren Raz , Marija Vucelja

Langer theory of metastability provides a description of the lifetime and properties of the metastable phase of the Ising model field-driven transition, describing the magnetic field-driven transition in ferromagnets and the chemical…

Statistical Mechanics · Physics 2015-06-19 Miguel Ibáñez Berganza , Pietro Coletti , Alberto Petri

We consider the thermal relaxation of a particle in a piecewise-constant potential landscape subject to thermal fluctuations in the overdamped limit. We study the connection between the occurrence of the Mpemba effect, the presence of…

Statistical Mechanics · Physics 2021-12-08 Matthew Walker , Marija Vucelja

We investigate temperature quenches across the reentrant phase transition of the antiferromagnetic Ising model in a magnetic field and show that the strong direct and inverse Mpemba effects arise when quenches terminate in the paramagnetic…

Statistical Mechanics · Physics 2026-05-01 Kristian Blom , Doron Benyamin , Uwe Thiele , Oren Raz , Aljaz Godec

The behavior of systems far from equilibrium is often complex and unpredictable, challenging and sometimes overturning the physical intuition derived from equilibrium scenarios. One striking example of this is the Mpemba effect, which…

Quantum Physics · Physics 2025-04-02 Stefano Longhi

We measure the relaxation time of a square lattice Ising ferromagnet that is quenched to zero-temperature from supercritical initial conditions. We reveal an anomalous and seemingly overlooked timescale associated with the relaxation to…

Statistical Mechanics · Physics 2020-10-26 James Denholm , Ben Hourahine

The Mpemba effect, an example of anomalous thermal relaxations, occurs when a system prepared at a hot temperature overtakes an identical system prepared at a warm temperature and cools down faster to the environment's temperature. We study…

Statistical Mechanics · Physics 2023-08-10 Saikat Bera , Matthew R. Walker , Marija Vucelja

We study the equilibrium and dynamic phase transition properties of two-dimensional Ising model on a decorated triangular lattice under the influence of a time-dependent magnetic field composed of a periodic square wave part plus a time…

Statistical Mechanics · Physics 2023-07-25 Yusuf Yüksel

We consider a Glauber dynamics associated with the Ising model on a large two-dimensional box with with minus boundary conditions and in the limit of a vanishing positive external magnetic field. The volume of this box increases…

Probability · Mathematics 2020-05-13 Alexandre Gaudillière , Paolo Milanesi , Maria Eulália Vares

We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous…

Statistical Mechanics · Physics 2023-01-03 Sudip Mukherjee , Abhik Basu

The Mpemba effect refers to systems whose thermal relaxation time is a non-monotonic function of the initial temperature. Thus, a system that is initially hot cools to a bath temperature more quickly than the same system, initially warm. In…

Statistical Mechanics · Physics 2021-03-31 Raphaël Chétrite , Avinash Kumar , John Bechhoefer

The Mpemba effect (a counterintuitive thermal relaxation process where an initially hotter system may cool down to the steady state sooner than an initially colder system) is studied in terms of a model of inertial suspensions under shear.…

Statistical Mechanics · Physics 2021-03-10 Satoshi Takada , Hisao Hayakawa , Andrés Santos

We study the phase diagram of the two-dimensional repulsive Hubbard model with spin-dependent anisotropic hopping at half-filling. The system develops Ising antiferromagnetic long-range order already at infinitesimal repulsive interaction…

Strongly Correlated Electrons · Physics 2017-05-17 Jan Gukelberger , Lei Wang , Lode Pollet

The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the…

The counterintuitive Mpemba effect, wherein a hotter system cools faster, critically lacks a general macroscopic theory. Here, starting from linear irreversible thermodynamics, we formulate a generalized Newton's cooling law,…

Statistical Mechanics · Physics 2026-05-21 Yun-Qian Lin , Z. C. Tu , Yu-Han Ma
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