arXiv subjects

Marija Vucelja

Publications and source records attributed to Marija Vucelja.

18 recordsLinked to original sources

arXiv2026

Thermalization packets and optimal ice cubes

Relaxation toward equilibrium is usually accelerated by modifying the environment or by cooling a system further from equilibrium. Here we introduce a distinct strategy: thermalization packets, auxiliary systems prepared in advance and later coupled to a target system to accelerate its relaxation toward a prescribed thermal state. Thus, thermalization packets trade preparation effort for reduced waiting time. When the objective is cooling, we colloquially refer to such packets as ice cubes. Unlike ordinary coolants, thermalization packets are characterized not only by their temperature or heat capacity, but also by their microscopic preparation. We define perfect and optimal packets by their ability to suppress the slowest relaxation mode of the coupled dynamics: perfect packets eliminate it entirely, while optimal packets minimize its amplitude. We show that, under generic conditions, perfect packets exist among thermal preparations near equilibrium. Surprisingly, for asymptotic relaxation, the optimum among thermal preparations is generally not the coldest packet: cooling the packet beyond the slow-mode-cancelling optimum restores a nonzero slow mode and can therefore slow relaxation, yielding a packet analog of the Mpemba effect. We demonstrate the concept in exactly solvable Metropolis dynamics, a minimal two-qubit model, and a boundary-coupled interacting Ising-spin system. We also extend the framework to packets optimized for finite readout times. Finally, we show that the perfect-packet contour can connect the trivial bath-equilibrium point to a nontrivial strong Mpemba or strong inverse-Mpemba point.

cond-mat.stat-mech↗

arXiv2026

Extending the Mpemba effect to the underdamped realm

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.

cond-mat.stat-mech↗

arXiv2025

Speedups in nonequilibrium thermal relaxation: Mpemba and related effects

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.

cond-mat.stat-mech↗

arXiv2023

Effect of dynamics on anomalous thermal relaxations and information exchange

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 the Mpemba effect in Markov jump processes on linear reaction networks as a function of the relaxation dynamics. The dynamics are characterized by a load distribution factor introduced to control the transition rates in a manner that obeys detailed balance. We provide analytical results and insights on when the Mpemba effect happens in the unimolecular reactions of three species as a function of the dynamics. In particular, we derive that the regions of the Strong Mpemba effect in cooling and heating are non-overlapping and that there is, at most, a single Strong Mpemba temperature. Next, we illustrate our results on a Maxwell demon setup, where we show that one can utilize the strong variant of the Mpemba effect to have shorter cycles of the Maxwell demon device, leading to increased power output, and stable device operation, without sacrificing efficiency.

cond-mat.stat-mech↗

arXiv2023

Optimal transport and anomalous thermal relaxations

We study connections between optimal transport and anomalous thermal relaxations. A prime example of anomalous thermal relaxations is the Mpemba effect, which occurs when a hot system overtakes an identical warm system and cools down faster. Conversely, optimal transport is a resource-efficient way to transport the source distribution to a target distribution in a finite time. By "a resource-efficient way," what is often meant is with the least amount of entropy production. Our paradigm for a continuum system is a particle diffusing on a potential landscape, while for a discrete system, we use a three-state Markov jump process. In the continuous case, the Mpemba effect is generically associated with high entropy production. As such, at large yet finite times, the system evolution toward the target is not optimal in this respect. However, in the discrete case, we show that for specific dynamics, the optimal transport and the strong variant of the Mpemba effect can occur for the same relaxation protocol.

cond-mat.stat-mech↗

arXiv2023

Mpemba effect in terms of mean first passage time

The Mpemba effect occurs when a system prepared at a hot temperature cools down faster to the bath temperature than an identical system starting at a warm temperature. We derive the condition for the Mpemba effect in the small-diffusion limit of overdamped Langevin dynamics on a double-well potential. Our results show the strong Mpemba effect occurs when the probability of being in a well at initial and bath temperature match, which agrees with experiments. We also derive the conditions for the weak Mpemba effect and express the conditions for the effects in terms of mean first passage time.

cond-mat.stat-mech↗

arXiv2021

Nonreversible Markov chain Monte Carlo algorithm for efficient generation of Self-Avoiding Walks

We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal algorithm introduced by H.~Hu, X.~Chen, and Y.~Deng in \cite{old}, while for three-dimensional walks, it is 3--5 times faster. The new algorithm introduces nonreversible Markov chains that obey global balance and allows for three types of elementary moves on the existing self-avoiding walk: shorten, extend or alter conformation without changing the walk's length.

cond-mat.stat-mech↗

arXiv2021

Anomalous thermal relaxation of Langevin particles in a piecewise-constant potential

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 metastable states, and phase transitions as a function of the potential. We find that the Mpemba effect exists even in cases without metastable states. In the considered physical system, the borders of the areas where the effect happens correspond to either eigenvector changes of direction or to phase transitions. Finally, we discuss the topological aspects of the strong Mpemba effect and propose using topology to search for the Mpemba effect in a physical system.

cond-mat.stat-mech↗

arXiv2018

Solution of the Metropolis dynamics on a complete graph with application to the Markov chain Mpemba effect

We find analytically the complete set of eigenvalues and eigenvectors associated with Metropolis dynamics on a complete graph. As an application, we use this information to study a counter-intuitive relaxation phenomenon, called the Mpemba effect. This effect describes situations when upon performing a thermal quench, a system prepared in equilibrium at high temperatures relaxes faster to the bath temperature than a system prepared at a temperature closer to that of the bath. We show that Metropolis dynamics on a complete graph does not support weak nor strong Mpemba effect, however, when the graph is not complete, the effect is possible.

math-ph↗

arXiv2018

The Mpemba index and anomalous relaxation

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 non-monotonic relaxations were observed in various systems, including water, magnetic alloys, polymers, and driven granular gases. We analyze the Mpemba effect in Markovian dynamics and discover that a stronger version of the effect often exists for a carefully chosen set of initial temperatures. In this \emph{strong Mpemba effect}, the relaxation time jumps to a smaller value leading to exponentially faster equilibration dynamics. The number of such special initial temperatures defines the \emph{Mpemba index}, whose parity is a topological property of the system. To demonstrate these concepts, we first analyze the different types of Mpemba relaxations in the mean field anti-ferromagnet Ising model, which demonstrates a surprisingly rich Mpemba phase diagram. Moreover, we show that the strong effect survives the thermodynamic limit and that it is tightly connected with thermal overshoot -- in the relaxation process, the temperature of the relaxing system can decay non-monotonically as a function of time. Using the parity of the Mpemba index, we then study the occurrence of the strong Mpemba effect in a large class of thermal quench processes and show that it happens with non-zero probability even in the thermodynamic limit. This is done by introducing the \emph{isotropic} model for which we obtain analytical lower bound estimates for the probability of the strong Mpemba effects. Consequently, we expect that such exponentially faster relaxations can be observed experimentally in a wide variety of systems.

cond-mat.stat-mech↗

arXiv2018

Memory effect and phase transition in a hierarchical trap model for spin glass

We introduce an efficient dynamical tree method that enables us, for the first time, to explicitly demonstrate thermo-remanent magnetization memory effect in a hierarchical energy landscape. Our simulation nicely reproduces the nontrivial waiting-time and waiting-temperature dependences in this non-equilibrium phenomenon. We further investigate the condensation effect, in which a small set of micro-states dominates the thermodynamic behavior, in the multi-layer trap model. Importantly, a structural phase transition of the tree is shown to coincide with the onset of condensation phenomenon. Our results underscore the importance of hierarchical structure and demonstrate the intimate relation between glassy behavior and structure of barrier trees.

cond-mat.dis-nn↗

arXiv2017

Dynamics of adaptive immunity against phage in bacterial populations

The CRISPR (clustered regularly interspaced short palindromic repeats) mechanism allows bacteria to adaptively defend against phages by acquiring short genomic sequences (spacers) that target specific sequences in the viral genome. We propose a population dynamical model where immunity can be both acquired and lost. The model predicts regimes where bacterial and phage populations can co-exist, others where the populations exhibit damped oscillations, and still others where one population is driven to extinction. Our model considers two key parameters: (1) ease of acquisition and (2) spacer effectiveness in conferring immunity. Analytical calculations and numerical simulations show that if spacers differ mainly in ease of acquisition, or if the probability of acquiring them is sufficiently high, bacteria develop a diverse population of spacers. On the other hand, if spacers differ mainly in their effectiveness, their final distribution will be highly peaked, akin to a "winner-take-all" scenario, leading to a specialized spacer distribution. Bacteria can interpolate between these limiting behaviors by actively tuning their overall acquisition probability.

physics.bio-ph↗

arXiv2016

Lifting -- A nonreversible Markov chain Monte Carlo Algorithm

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ reversible Markov chains. Reversible chains obey detailed balance and thus ensure that the system will eventually relax to equilibrium. Detailed balance is not necessary for convergence to equilibrium. We review nonreversible Markov chains, which violate detailed balance, and yet still relax to a given target stationary distribution. In particular cases, nonreversible Markov chains are substantially better at sampling than the conventional reversible Markov chains with up to a square root improvement in the convergence time to the steady state. One kind of nonreversible Markov chain is constructed from the reversible ones by enlarging the state space and by modifying and adding extra transition rates to create non-reversible moves. Because of the augmentation of the state space, such chains are often referred to as lifted Markov Chains. We illustrate the use of lifted Markov chains for efficient sampling for several examples. The examples include sampling on a ring, sampling on a torus, the Ising model on a complete graph, and the one-dimensional Ising model. We also provide a pseudocode implementation, review related work, and discuss the applicability of such methods.

cond-mat.stat-mech↗

arXiv2015

Extreme value statistics of work done in stretching a polymer in a gradient flow

We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the Large Deviation Function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: "near tails" are linear in work and dominated by coiled polymer configurations, while "far tails" are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several singular elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition.

cond-mat.stat-mech↗

arXiv2012

Emergence of clones in sexual populations

In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection, populations consist of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, which is realized for example in the facultatively sexual populations that outcross in only a fraction of reproductive cycles, selection can amplify individual genotypes into large clones. Such clones emerge when the fitness advantage of some of the genotypes is large enough that they grow to a significant fraction of the population despite being broken down by recombination. The occurrence of this "clonal condensation" depends, in addition to the outcrossing rate, on the heritability of fitness. Clonal condensation leads to a strong genetic heterogeneity of the population which is not adequately described by traditional population genetics measures, such as Linkage Disequilibrium. Here we point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy we explicitly calculate the probability, Y, that two individuals are genetically identical as a function of the key parameters of the model. While Y is the analog of the spin-glass order parameter, it is also closely related to rate of coalescence in population genetics: Two individuals that are part of the same clone have a recent common ancestor.

q-bio.PE↗

arXiv2011

Fractal iso-contours of passive scalar in smooth random flows

We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new effective semi-analytic algorithm to model the scalar turbulence. We then carry massive numerics of passive scalar turbulence with the focus on the statistics of nodal lines. The distribution of contours over sizes and perimeters is shown to depend neither on the flow realization nor on the resolution (diffusion) scale $r_d$ for scales exceeding $r_d$. The scalar isolines are found fractal/smooth at the scales larger/smaller than the pumping scale $L$. We characterize the statistics of bending of a long isoline by the driving function of the Löwner map, show that it behaves like diffusion with the diffusivity independent of resolution yet, most surprisingly, dependent on the velocity realization and the time of scalar evolution.

math-ph↗

arXiv2008

Irreversible Monte Carlo Algorithms for Efficient Sampling

Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is sufficient but not necessary. We construct irreversible deformation of a given reversible algorithm capable of dramatic improvement of sampling from known distribution. Our transformation modifies transition rates keeping the structure of transitions intact. To illustrate the general scheme we design an Irreversible version of Metropolis-Hastings (IMH) and test it on example of a spin cluster. Standard MH for the model suffers from the critical slowdown, while IMH is free from critical slowdown.

cond-mat.stat-mech↗

arXiv2004

Quantum lithography by coherent control of classical light pulses

The smallest spot in optical lithography and microscopy is generally limited by diffraction. Quantum lithography, which utilizes interference between groups of N entangled photons, was recently proposed to beat the diffraction limit by a factor N. Here we propose a simple method to obtain N photons interference with classical pulses that excite a narrow multiphoton transition, thus shifting the "quantum weight" from the electromagnetic field to the lithographic material. We show how a practical complete lithographic scheme can be developed and demonstrate the underlying principles experimentally by two-photon interference in atomic Rubidium, to obtain focal spots that beat the diffraction limit by a factor of 2.

quant-ph↗