We introduce a validation process that harnesses engineered many-body relaxation to control and calibrate quantum hardware. On two independently developed neutral-atom processors, we realize the many-body quantum Mpemba effect in an open system for the first time. Initial-state engineering creates fast and slow relaxation pathways: the fast pathway opens access to unreachable mixed-state physics before hardware noise obscures the target dynamics, whereas the slow pathway amplifies hidden imperfections in preparation and control. Computational-basis measurements directly and independently benchmark dynamical reliability, revealing each processor's actual operating window as a many-body simulator. The processors are thus judged by the very dynamics they are built to reproduce. Complementary responses disentangle control errors and drive an adaptive, time-resolved scheme that supplies hardware developers directly actionable corrections, enhancing faithful reproduction of the target dynamics. These results establish many-body relaxation as a transferable validation and calibration tool for programmable quantum processors.

We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency detuning, synchronization is enhanced. The coupling scheme induces a change in criticality, driving the system from a continuous phase transition to an explosive transition by changing a single parameter. Our work offers a general route to efficient synchronization in engineered networks and provides insight into the critical behavior of the Kuramoto model.

Critical phenomena at finite temperature underpin a broad range of physical systems, yet their study remains challenging due to computational bottlenecks near phase transitions. Quantum annealers have attracted significant interest as a potential tool for accessing finite temperature criticality beyond classical reach, but their utility in precisely resolving criticality has remained limited by noise, hardware constraints, and thermal fluctuations. Here we overcome these challenges, introducing a sampling protocol that combines real-time temperature inference with fine control of the energy scales throughout experiments. A careful embedding strategy allows us to fully capture the finite-temperature critical behavior of the paradigmatic two-dimensional Ising ferromagnet on toroidal lattices up to 2640 spins. By tuning the energy scale of the system and mitigating device defects, we sample effective Boltzmann distributions extracting both the critical temperature and the associated universal critical exponents. Our approach opens the study of equilibrium and non-equilibrium critical phenomena in a broad class of systems at finite temperature.

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 phase. These anomalous relaxation phenomena originate from the selective excitation of the slowest relaxation mode, which in the paramagnetic phase is purely staggered. Consequently, quenches starting from the paramagnetic phase have zero overlap with the slow mode and exhibit a strong (inverse) Mpemba effect. Quenches from the antiferromagnetic phase excite the staggered mode and display a slow-relaxation tail. By varying the lattice coordination number we show that the strong Mpemba effect disappears in the absence of reentrance. Our results provide the first demonstration of the strong (inverse) Mpemba effect in the antiferromagnetic Ising model based on the pair-approximation, and establish a link between anomalous relaxation and the equilibrium phase behavior.

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 can occur. A prime example of anomalous thermal relaxation is the Mpemba effect, in which a system prepared at a hot temperature cools down to the temperature of the cold environment faster than an identical system prepared at a warm temperature. Although reported for water more than 2000 years ago by Aristotle, the recent observations of analogous relaxation speedups in a variety of systems have motivated the search for general explanations. We review anomalous relaxation effects, which all share a nonmonotonic dependence of relaxation time versus initial “distance" from the final state or from the phase transition. The final state can be an equilibrium or a nonequilibrium steady state. We first review the water experiments and classify the anomalous relaxation phenomena related to the Mpemba effect. We then provide a modern definition of the Mpemba effect, focusing on the theoretical frameworks of stochastic thermodynamics, kinetic theory, Markovian dynamics, and phase transitions. We discuss the recent experimental and numerical developments that followed these theoretical advances. These developments paved the way for the prediction and observation of novel phenomena, such as the inverse Mpemba effect. The review is self-contained and introduces anomalous relaxation phenomena in single- and many-body systems, both classical and quantum. We also discuss the broader relevance of the Mpemba effect, including its relation with phase transitions and its experimental implications. We end with perspectives that connect anomalous speedups to ideas for designing optimal heating/cooling protocols, heat engines, and efficient samplers.

The Mpemba effect is the counterintuitive phenomenon in which an initially hotter system cools faster than a colder, otherwise identical system. It has been experimentally demonstrated in various classical overdamped systems. Here, we explore the existence of the same effect in a regime where inertia cannot be neglected, namely, the underdamped regime. We consider the underdamped dynamics of a Brownian particle in a potential. We show perturbatively that, if the effect exists in the overdamped limit, it persists for sufficiently large but finite damping. In the ultra-weak-damping limit, we show that the effect cannot occur for smooth confining single-well potentials with canonical initial states, but can arise in more complex potentials. We demonstrate our results numerically using double-well potentials, the canonical setting for the Mpemba effect in the overdamped limit.

Shortcuts to adiabaticity are strategies for conserving adiabatic invariants under nonadiabatic (i.e. fast-driving) conditions. Here, we show how to extend classical, Hamiltonian shortcuts to adiabaticity to allow the crossing of a phase-space separatrix-a situation in which a corresponding adiabatic protocol does not exist. Specifically, we show how to construct a time-dependent Hamiltonian that evolves one energy shell to another energy shell across a separatrix. Leveraging this method, we design an erasure procedure whose energy cost bound and fidelity do not depend on the protocol's duration.

A common approach to quantify excess dissipation in slowly driven thermodynamic processes is through the use of a Riemannian metric on the space of control parameters, where optimal driving protocols follow geodesics. Near phase transitions, this geometric picture breaks down as the metric diverges and geodesics may cease to exist. Using Widom scaling, we analyze this framework for several universality classes and show that in some cases the thermodynamic length across the phase transition remains finite. We then demonstrate a numerical approach for computing minimal paths in such systems. We show that, in some regimes, the shortest path crosses the phase transition - even when alternative paths confined to a single phase exist.

The Mpemba effect is a counterintuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here, we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e., due to interference effects. We experimentally demonstrate our findings on a single ^{88}Sr^{+} trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.

The hypothalamo-neurohypophyseal system is an important neuroendocrine brain-to-blood conduit through which the neurohormones oxytocin and arginine-vasopressin are released from the brain into the general circulation to affect peripheral physiological functions such as salt balance, metabolism and reproduction. However, whether an active mechanism executes fast and efficient neurohormone release to the periphery remains unsolved. We show that a hyperosmotic physiological challenge elicits a local increase in neurohypophyseal blood flow velocities and a change in capillary diameter, which is dictated by the geometry of the hypophyseal vascular microcircuit. Genetic ablation of oxytocin neurons and inhibition of oxytocin receptor signaling attenuated capillary blood flow and diameter. Optogenetic stimulation of oxytocin neurons resulted in an oxytocin receptor-dependent increase in blood flow velocities. Lastly, both osmotic challenge and oxytocin neuronal activation elicited a local rise in neurohypophyseal capillary permeability in an oxytocin signaling-dependent manner. Our study demonstrates that physiologically elicited changes in neurohypophyseal blood flow and permeability are regulated by oxytocin. We propose that oxytocin-dependent neuro-vascular coupling facilitates its efficient uptake into the blood circulation, suggesting a self-perpetuating mechanism of peripheral hormone transfer. ### Competing Interest Statement The authors have declared no competing interest.

We calculate the average number of critical points N[over ¯] of the energy landscape of a many-body system with disordered two-body interactions and a weak on-site potential. We find that introducing a weak nonlinear on-site potential dramatically increases N[over ¯] to exponential in system size and give a complete picture of the organization of critical points. Our results extend solvable spin-glass models to physically more realistic models and are of relevance to glassy systems, nonlinear oscillator networks, and many-body interacting systems.

When a system's parameter is abruptly changed, a relaxation toward the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation operator results in a singularity in the dynamics analogous to a first-order equilibrium phase transition. While dynamical phase transitions are intrinsically hard to detect in nature, here we show how this kind of transition can be observed in an experimentally feasible four-state colloidal system. Finally, analytical proof of survival in the thermodynamic limit of a many body (1D Ising) model is provided.

The Landauer principle sets a thermodynamic bound of k(B)T ln 2 on the energetic cost of erasing each bit of information. It holds for any memory device, regardless of its physical implementation. It was recently shown that carefully built artificial devices can attain this bound. In contrast, biological computation-like processes, e.g., DNA replication, transcription and translation use an order of magnitude more than their Landauer minimum. Here, we show that reaching the Landauer bound is nevertheless possible with biological devices. This is achieved using a mechanosensitive channel of small conductance (MscS) from E. coli as a memory bit. MscS is a fast-acting osmolyte release valve adjusting turgor pressure inside the cell. Our patch-clamp experiments and data analysis demonstrate that under a slow switching regime, the heat dissipation in the course of tension-driven gating transitions in MscS closely approaches its Landauer limit. We discuss the biological implications of this physical trait.

When a hot system cools down faster than an equivalent cold one, it exhibits the Mpemba effect (ME). This counterintuitive phenomenon was observed in several systems including water, magnetic alloys, and polymers. In most experiments the system is coupled to the bath through its boundaries, but all theories so far assumed bulk coupling. Here we build a general framework to characterize anomalous relaxations through boundary coupling, and present two emblematic setups: a diffusing particle and an Ising antiferromagnet. In the latter, we show that the ME can survive even arbitrarily weak couplings.

It is commonly assumed that a large system, weakly coupled to a thermal environment through its boundaries, relaxes quasistatically towards the new equilibrium even when the temperature of the environment changes abruptly. Here we show how this intuitive picture can break down for discrete energy systems, even in the case of infinitely weak coupling. We provide an example in the Ising chain, showing how the interaction among degrees of freedom can create corrugated energy landscapes that are responsible for far-from-equilibrium and allow anomalous relaxation effects to survive infinitely weak couplings.

The echo-chamber effect is a common term in opinion dynamic modeling to describe how a person's opinion might be artificially enhanced as it is reflected back at her through social interactions. Here, we study the existence of this effect in statistical mechanics models, which are commonly used to study opinion dynamics. We show that the Ising model does not exhibit echo-chambers, but this result is a consequence of a special symmetry. We then distinguish between three types of models: (i) those with a strong echo-chamber symmetry, that have no echo-chambers at all; (ii) those with a weak echo-chamber symmetry that can exhibit echo-chambers but only if there are external fields in the system, and (iii) models without echo-chamber symmetry that generically have echo-chambers. We use these results to construct an efficient algorithm to efficiently and precisely calculate magnetization in arbitrary tree networks. Finally, We apply this algorithm to study two systems: phase transitions in the random field Ising model on a Bethe lattice and the influence optimization problem in social networks.

Probability current fluctuations play an important role in nonequilibrium statistical mechanics, and are a key object of interest in both theoretical studies and in practical applications. So far, most of the studies were devoted to the fluctuations of the time-averaged probability current, the zero-frequency Fourier component of the time-dependent current. However, in many practical applications the fluctuations at other frequencies are of equal importance. Here we study the statistics of all the probability current's Fourier component in periodically driven stochastic systems. We restrict our study to ``trapped'' systems where the degrees of freedom of the system cannot achieve arbitrarily large values as time becomes large, in contrast to, e.g., diffusing systems. First, we discuss possible methods to calculate the current statistics, valid even when the current's Fourier frequency is incommensurate with the driving frequency, breaking the time periodicity of the system. Somewhat surprisingly, we find that the cumulant generating function (CGF), that encodes all the statistics of the current, is composed of a continuous background at any frequency accompanied by either positive or negative discontinuities at current's frequencies commensurate with the driving frequency. We show that cumulants of increasing orders display discontinuities at an increasing number of locations but with decreasing amplitudes that depend on the rational frequency ratio. All these discontinuities are then transcribed in the behavior of the CGF. As the measurement time increases, these discontinuities become sharper but keep the same amplitude and eventually lead to discontinuities of the CGF at all the frequencies that are commensurate with the driving frequency in the limit of infinitely long measurement. We demonstrate our formalism and its consequences on three types of models: an underdamped Brownian particle in a periodically driven harmonic potential; a periodically driven run-and-tumble particle; and a two-state system. Our results show a rich and interesting structure in experimentally accessible and important objects: the fluctuations of alternating currents as a function of their frequency.

Finding the ground state of an Ising spin glass on general graphs belongs to the class of NP-hard problems, widely believed to have no efficient polynomial-time algorithms to solve them. An approach developed in computer science for dealing with such problems is to devise approximation algorithms; these are algorithms, whose run time scales polynomially with the input size, that provide solutions with provable guarantees on their quality in terms of the optimal unknown solution. Recently, several algorithms for the Ising spin-glass problem on a bounded degree graph that provide different approximation guarantees were introduced. D-Wave, a Canadian-based company, has constructed a physical realization of a quantum annealer and has enabled researchers and practitioners to access it via their cloud service. D-Wave is particularly suited for computing an approximation for the ground state of an Ising spin glass on its Chimera and Pegasus graphs-both with a bounded degree. To assess the quality of D-Wave's solution, it is natural to compare it to classical approximation algorithms specifically designed to solve the same problem. In this work, we compare the performance of a recently developed approximation algorithm to solve the Ising spin-glass problem on graphs of bounded degree against the performance of the D-Wave computer. We also compared the performance of D-Wave's computer in the Chimera architecture against the performance of a heuristic tailored specifically to handle the Chimera graph. We found that the D-Wave computer was able to find better approximations for all the random instances of the problem we studied-Gaussian weights, uniform weights, and discrete binary weights. Furthermore, the convergence times of D-Wave's computer were also significantly better. These results indicate the merit of D-Wave's computer under certain specific instances. More broadly, our method is relevant to a wider class of performance comparison studies, and we suggest that it is important to compare the performance of quantum computers not only against exact classical algorithms with exponential run-time scaling, but also against approximation algorithms with polynomial run-time scaling and a provable guarantee of performance.

Non-Hermitian Hamiltonians, and particularly parity-time (PT) and anti-PT symmetric Hamiltonians, play an important role in many branches of physics, from quantum mechanics to optical systems and acoustics. Both the PT and anti-PT symmetries are specific instances of a broader class known as anyonic-PT symmetry, where the Hamiltonian and the PT operator satisfy a generalized commutation relation. Here, we study theoretically these novel symmetries and demonstrate them experimentally in coupled lasers systems. We resort to complex coupling of mixed dispersive and dissipative nature, which allows unprecedented control on the location in parameter space where the symmetry and symmetry breaking occur. Moreover, tuning the coupling in the same physical system allows us to realize the special cases of PT and anti-PT symmetries. In a more general perspective, we present and experimentally validate a new relation between laser synchronization and the symmetry of the underlying non-Hermitian Hamiltonian.