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The parametric cubic van der Waals polynomial $p V^3 - (R T + b p) V^2 + a V - a b$ is analysed mathematically and some new generic features (theoretically, for any substance) are revealed - if the pressure is not allowed to take negative values [temperatures not lower than $1/(4Rb)$], the localization intervals of the... |
Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability {\it a priori} where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's and Gibbs' entropy arises in the limit of infinitely repeated observation... |
Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical ... |
We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which ... |
The magnetic properties of the mixed spin-$\frac{1}{2}$ and spin-$\frac{7}{2}$ Ising model with a crystal-field in a longitudinal magnetic field are investigated on the Bethe lattice using exact recursion relations. The ground-state phase diagram is constructed. |
We review the main result of <a href="https://arxiv.org/abs/cond-mat/0503564" data-arxiv-id="cond-mat/0503564" class="link-https">cond-mat/0503564</a>. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the $sl_2$ loop algebra symmetry if the $q$ parameter is given by a root of u... |
Random walks are frequently used as a model for very diverse physical phenomena. The Monte Carlo method is a versatile tool for the study of the properties of systems modelled as random walks. |
We observe that space- and time-crystallization effects in multicomponent superfluids---while having the same physical origin and mathematical description as in the single-component case---are conceptually much more straightforward. Specifically, the values of the temporal and spatial periods are absolute rather than r... |
We study the simplest model of dynamic heterogeneities in glass forming liquids: one-spin facilitated kinetic Ising model introduced by Fredrickson and Andersen [G.H. Fredrickson and H.C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, 5822 (1985)]. We show that the low-temperature, long-time behavior o... |
We use LINUS, a procedure developed by Srinivasan and Rose, to provide a physical interpretation of and to predict the secondary structures of proteins. The secondary structure type at a given site is identified by the largest conformational bias during short time simulations. |
We study the simplest irreversible ballistically-controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents characterizing the density and typical velocity decay are explicitly worked out... |
The spherical $p$-spin is a fundamental model for glassy physics, thanks to its analytic solution achievable via the replica method. Unfortunately the replica method has some drawbacks: it is very hard to apply to diluted models and the assumptions beyond it are not immediately clear. |
We discuss continuous cascade models and their potential for modelling the energy dissipation in a turbulent flow. Continuous cascade processes, expressed in terms of stochastic integrals with respect to Lévy bases, are examples of ambit processes. |
A new approach to the understanding of complex behavior of financial markets index using tools from thermodynamics and statistical physics is developed. Physical complexity, a magnitude rooted in Kolmogorov-Chaitin theory is applied to binary sequences built up from real time series of financial markets indexes. |
We show that the flocking transition in the Vicsek model is best understood as a liquid-gas transition, rather than an order-disorder one. The full phase separation observed in flocking models with Z2 rotational symmetry is, however, replaced by a microphase separation leading to a smectic arrangement of traveling ord... |
Ground-state properties of the spin-1/2 and spin-1 Ising-Heisenberg model on doubly decorated planar lattices, are investigated in detail. On the basis of the mapping transformation method, we prove an existence of unusual quantum phases which occur due to the competition between Ising-type and XXZ anizotropic Heisenb... |
The entropy of a classical thermally isolated Hamiltonian system is given by the logarithm of the measure of phase space enclosed by the constant energy hyper-surface, also known as volume entropy. It has been shown that on average the latter cannot decrease if the initial state is sampled from a classical passive dis... |
In this paper we extend the encounter-based model of diffusion-mediated surface absorption to the case of an unbiased run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ and switching between two constant velocity states $\pm v$ at a rate $\alpha$. The encounter-based formalism is motivated by the obse... |
Restricted Boltzmann machines (RBM) and deep Boltzmann machines (DBM) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between them and tensor networks. |
The thermal scalar and vector potential were introduced to investigate the thermal transport under a temperature gradient in terms of linear response theory[1,2]. However, the microscopic origin of these phenomenological thermal potentials had not been addressed clearly. |
A Brownian information engine is a device extracting a mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. |
We present in this paper an exact study concerning a first order transition induced by an inhomogeneous boundary magnetic field in the 2D Ising model. From a previous analysis of the interfacial free energy in the discrete case (J. Phys. A, 2849, 2005), we identify, using an asymptotic expansion in the thermodynamic l... |
We study the entanglement content of a class of mesoscopic tunable magnetic systems. The systems are closed finite spin-1/2 chains with ferromagnetic nearest-neighbor interactions frustrated by antiferromagnetic next-nearest-neighbor interactions. |
Based on the exact solution of the eigenvalue problem for the $U_q[sl(2|1)]$ vertex model built from alternating 3-dimensional fundamental and dual representations by means of the algebraic Bethe ansatz we investigate the ground state and low energy excitations of the corresponding mixed superspin chain for deformation... |
Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. |
We derive the nonequilibrium transient state work fluctuation theorem and also the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics not only dissipative but also non-Markovian in general. |
We use large scale simulations to study interacting particles in two dimensions in the presence of both an ac drive and quenched disorder. As a function of ac amplitude, there is a crossover from a low drive regime where the colloid positions are highly disordered to a higher ac drive regime where the system dynamical... |
We investigate the final state of zero-temperature Ising ferromagnets which are endowed with single-spin flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. |
We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. |
The concept of random deaths in a computational model for population dynamics is critically examined. We claim that it is just an artifact, albeit useful, of computational models to limit the size of the populations and has no biological foundation. |
In this paper we study the properties of the quenched pressure of a multi-layer spin-glass model (a deep Boltzmann Machine in artificial intelligence jargon) whose pairwise interactions are allowed between spins lying in adjacent layers and not inside the same layer nor among layers at distance larger than one. We pro... |
The surrogate process approximation (SPA) is applied to model the nonequilibrium dynamics of a reaction coordinate (RC) associated with the unfolding and refolding processes of a deca-alanine peptide at 300 K. The RC dynamics, which correspond to the evolution of the end-to-end distance of the polypeptide, are produced... |
In a recent Letter [Phys. Rev. Lett. 79, 889 (1997) and <a href="https://arxiv.org/abs/cond-mat/9702054" data-arxiv-id="cond-mat/9702054" class="link-https">cond-mat/9702054</a>] we have demonstrated that the avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical results for te... |
The Kibble-Zurek (KZ) mechanism has been applied to a variety of systems ranging from low temperature Bose-Einstein condensations to grand unification scales in particle physics and cosmology and from classical phase transitions to quantum phase transitions. Here we show that finite-time scaling (FTS) provides a detai... |
We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show that the system undergoes a noise-induced reentrant transition in a given range... |
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. |
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as density profiles and spatial and temporal correlation functions for models with ... |
We calculate the response of a molecular magnet subject to a time-varying magnetic field and coupled to a heat bath. We propose that observations of calculated oscillations transverse to the field direction may be an effective way of demonstrating quantum tunneling and thus probing the details of level repulsion. |
We extend one dimensional asymmetric simple exclusion process (ASEP) to a surface and show that the effect of transverse diffusion is to induce a continuous phase transition from a constant density phase to a maximal current phase as the forward transition probability $p$ is tuned. The signature of the nonequilibrium ... |
We study the steady state of a multiply-connected system that is driven out of equilibrium by a sparse perturbation. The prototype example is an $N$-site ring coupled to a thermal bath, driven by a stationary source that induces transitions with log-wide distributed rates. |
We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. |
We suggested a method to estimate the quantum depletion of interacting Bose particles confined by a three dimensional harmonic trap. |
We apply the non-perturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called ``parity conserving'' or, more properly, ``generalized voter'' class) which is out of the reach of perturbative approaches. We show the existence of a genuinely non-perturbative... |
Percus showed that approximate theories for the structure of nonuniform hard sphere fluids can be generated by linear truncations of functional expansions of the nonuniform density rho (r) about that of an appropriately chosen uniform system. We consider the most general such truncation, which we refer to as the shift... |
We consider unsteady ballistic heat transport in a semi-infinite Hooke chain with a free end and an arbitrary heat source. An analytical description of the evolution of the kinetic temperature is proposed in both discrete (exact) and continuum (approximate) formulations. |
A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical and probabilistic behavior that is discussed here. |
In an effort to generalize the self-consistent Ornstein-Zernike approximation (SCOZA) -- an accurate liquid-state theory that has been restricted so far to hard-core systems -- to arbitrary soft-core systems we study a combination of SCOZA with a recently developed perturbation theory. The latter was constructed by Be... |
We introduce a novel family of translationally-invariant su$(m|n)$ supersymmetric spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing in particular the existence of a boson-fermion duality characteristic of this type of systems. |
We consider a growing network in which an incoming node gets attached to the $i^{th}$ existing node with the probability $\Pi_i \propto {k_i}^{\beta}\tau_i^{\alpha}$, where $k_{i}$ is the degree of the $i^{th}$ node and $\tau_i$ its present age. The phase diagram in the ${{\alpha}-{\beta}}$ plane is obtained. |
We study the scaling limit of planar loop erased random walk (LERW) on the percolation cluster, with occupation probability $p\geq p_c$. We numerically demonstrate that the scaling limit of planar LERW$_p$ curves, for all $p>p_c$, can be described by Schramm-Loewner Evolution (SLE) with a single parameter $\kappa$ ... |
We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). |
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process subordinated to a random time: it separately takes into account effects related to t... |
The balance equations for thermodynamic quantities are derived from the nonlocal quantum kinetic equation. The nonlocal collisions lead to molecular contributions to the observables and currents. |
We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. |
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the non-equilib... |
We have studied magnetic ordering in ferro/antiferromagnetic (F/AF) bilayers using Monte Carlo simulations of classical Heisenberg spins. For both flat and stepped interfaces we observed order in the AF above the Neel temperature, with the AF spins aligning collinearly with the F moments. |
When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled in such heterogeneous trajectories it becomes necessary to segment them by dete... |
Phonons are universal language for solid state theory. Effective phonon theory (self-consistent harmonic approximation) have been extensively used to access the weakly nonlinear effect in solid materials, which are standard content in textbook. |
Ordering of the frustrated classical Heisenberg model on the triangular-lattice with an incommensurate spiral spin structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the "skyrmion-lattice" state is observed in ... |
We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding natural action on measures and we prove that the iterated measure becomes asymptoti... |
We consider classical, interacting particles coupled to a thermal reservoir and subject to a local, time-varying potential while undergoing hops on a lattice. We impose detailed balance on the hopping rates and map the dynamics to the Fock space Doi representation, from which we derive the Jarzynski and Crooks relatio... |
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. |
We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-Parisi-Zhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is found to be inconsistent with the nominal one. |
We formulate and prove the local twist version of the Yamanaka-Oshikawa-Affleck theorem, an extension of the Lieb-Schultz-Mattis theorem, for one-dimensional systems of quantum particles or spins. We can treat almost any translationally invariant system wth global $U(1)$ symmetry. |
Magnetocaloric effect in a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with three equivalent lattice sites available for mobile electrons, is exactly investigated by considering the one-third electron filling and the ferromagnetic Ising exchange inter... |
We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. |
Continuous-time quantum Monte Carlo refers to a class of algorithms designed to sample the thermal distribution of a quantum Hamiltonian through exact expansions of the Boltzmann exponential in terms of stochastic trajectories which are periodic in imaginary time. Here, we show that for (sign-problem-free) quantum man... |
I develop a transfer matrix algorithm for computing the exact partition function of a square lattice polymer with nearest-neighbor interaction, by extending a previous algorithm for computing the total number of self-avoiding walks. The computation time scales as ~1.6^N with the chain length N, in contrast to the expl... |
We consider an Ising model where longitudinal components of every pair of spins have antiferromagnetic interaction of the same magnitude. When subjected to a transverse magnetic field at zero temperature, the system undergoes a phase transition of second order to an ordered phase and if the temperature is now increase... |
We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. |
We give a sufficient condition on a family of radial parametrized long-range potentials for a compact local minimality of a given $d$-dimensional Bravais lattice for its total energy of interaction created by each potential. This work is widely inspired by the paper of F. Theil about two dimensional crystallization. |
Motivated by the problem of sorting, we introduce two simple combinatorial models with distinct Hamiltonians yet identical spectra (and hence partition function) and show that the local dynamics of these models are very different. After a deep quench, one model slowly relaxes to the sorted state whereas the other mode... |
We analyze the condensation phase transitions in out-of-equilibrium complex networks in a unifying framework which includes the nonlinear model and the fitness model as its appropriate limits. We show a novel phase structure which depends on both the fitness parameter and the nonlinear exponent. |
Recently van der Meer et al. studied the breakdown of a granular cluster (Phys. Rev. Lett. |
The exact transfer-matrix solution for the longitudinal equilibrium properties of the single-file hard-disk fluid is used to study the limiting low- and high-pressure behaviors analytically as functions of the pore width. In the low-pressure regime, the exact third and fourth virial coefficients are obtained, which in... |
We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the Random First Order Transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual ... |
From the molecular dynamics simulation of a system of hard-core disks in which an equilibrium cell is connected with a nonequilibrium cell, it is confirmed that the pressure difference between two cells depends on the direction of the heat flux. From the boundary layer analysis, the velocity distribution function in t... |
A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. |
We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of offspring. We find that the uncentered PCA of datasets storing various system's... |
The maximum entropy principle in Tsallis statistics is reformulated in the mathematical framework of the q-product, which results in the unique non self-referential q-canonical distribution. As one of the applications of the present formalism, we theoretically derive the physical temperature which coincides with that ... |
The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for $N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian unitary ensemble GUE($N$), $N$-dimensional Gaussian symplectic ensemble GSE($N$), and Poisson... |
The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence of spanning sub-trees of two-component spanning trees. |
We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. |
We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. The field variable of the icosahedral model might take one of twelve vectors of unit length, which are given by the normalized vertices of the icosahedron, as value. |
In this work, we investigate thermodynamic properties of the one-dimensional (1D) spin-crossover molecular chain being a subject of a constant external pressure. Effective compressible degenerate Ising model is used as a theoretical framework. |
In response to W. G. Hoover's comment [<a href="https://arxiv.org/abs/1204.0312v2" data-arxiv-id="1204.0312v2" class="link-https">arXiv:1204.0312v2</a>] on our work [<a href="https://arxiv.org/abs/1203.5968" data-arxiv-id="1203.5968" class="link-https">arXiv:1203.5968</a>], we show explicitly that the divergence of... |
A new approach - nonequilibrium evolution thermodynamics, is compared with classical variant of Landau approach |
When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation of a reaction or, alternatively for the evolution of a population, should be extended by including non-Markovian memory effects. We consider the two cases of an external feedback, realized by fixed functions ... |
We study the nonequilibrium statistical mechanics of a finite classical system subjected to nongradient forces $\xi$ and maintained at fixed kinetic energy (Hoover-Evans isokinetic thermostat). We assume that the microscopic dynamics is sufficiently chaotic (Gallavotti-Cohen chaotic hypothesis) and that there is a nat... |
We study dynamics of a phase boundary in a one-dimensional lattice gas, which is initially put into a non-equilibrium configuration and then is let to evolve in time by particles performing nearest-neighbor random walks constrained by hard-core interactions. Initial non-equilibrium configuration is characterized by an... |
We show that any amount of anisotropy moves the Oslo model to another known universality class, the exponents of which can be derived exactly. This amounts to an exact solution of the quenched Edwards-Wilkinson equation with a drift term. |
Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are suffi... |
We investigate maximum efficiency at a given power for low-dissipation heat engines. Close to maximum power, the maximum gain in efficiency scales as a square root of relative loss in power and this scaling is universal for a broad class of systems. |
In sharp contrast to the corresponding classical systems cases it is not yet understood how to define a mechanical quantity with the interpretation of entropy creation rate for nonequilibrum stationary states of finite quantum systems with finite thermostats. Some aspects of this problem are discussed here in cases in... |
We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the non-interac... |
The entropic measure for analysis of grey level inhomogeneity (GLI) is proposed as a function of length scale. It allows us to quantify the statistical dissimilarity of the actual macrostate and the maximizing entropy of the reference one. |
We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented; one in the neighborhood of the vapor branch of the coexistence curve and the other being close to the critica... |
A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first ... |
The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase t... |
We generalize the momentum indicator idea taking into account the volume of transactions as a multiplicative factor. We compare returns obtained following strategies based on the classical or the generalized technical analysis, taking into account a sort of risk investor criterion. |
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