Heat capacity of isolated clusters

The character of interaction between thermal (vibrational) and configurational cluster excitations is considered under adiabatic conditions when a cluster is a member of a microcanonical ensemble. The hierarchy of equilibration times determines the character of atomic equilibrium in the cluster. The behavior of atoms in the cluster can be characterized by two effective (mean) temperatures, corresponding to the solid and liquid aggregate states, because the typical time for equilibration of atomic motion is less than the transition time between aggregate states. If the cluster is considered for a time much longer than the typical dwell time in either phase, then it is convenient to characterize the system by only one temperature, which is determined from the statistical-thermodynamic long-time average. These three temperatures are not far apart, nor are the cluster heat capacities evaluated on the basis of these definitions of temperature. The heat capacity of a microcanonical ensemble may be negative for two coexisting phases if the mean temperature is defined in terms of the mean kinetic energy, rather than as the derivative of energy with respect to microcanonical entropy. However, if the configurational excitation energy is smaller than the total excitation energy separating the phases, then the two-state model predicts a positive heat capacity under either definition of temperature. Moreover, if the cluster is sufficiently large, then the maximum values of the microcanonical and canonical heat capacities are equal.     

Violation of the zeroth law of thermodynamics in systems with negative specific heat

We show that systems with negative specific heat can violate the zeroth law of thermodynamics. By both numerical simulations and by using exact expressions for free energy and microcanonical entropy, it is shown that if two systems with the same intensive parameters but with negative specific heat are thermally coupled, they undergo a process in which the total entropy increases irreversibly. The final equilibrium is such that two phases appear; that is, the subsystems have different magnetizations and internal energies at temperatures which are equal in both systems, but that can be different from the initial temperature.     

Negative specific heat, phase transition and particles spilling from a potential well

For a finite number of noninteracting particles in a box with a potential well in the center, the microcanonical kinetic energy in dependence on the total energy as it is negative can be classified into three categories. The first exhibits a monotonical rise and the specific heat is positive. The second shows a diminishing sawtooth wave with a global rise. The last corresponds to the extreme case and takes the regular sawtooth wave form. The sawtooth wave portion associates periodically a kinetic energy fall in spite of an increase of the total energy; and we attribute to such a fall the negative specific heat. The phase transition can be defined when the relatively dense particle state in the well and relatively dilute particle state in the rest volume of the box coexist, and the appearance of the negative specific heat is sufficient but not necessary for the onset of the phase transition.     

Microcanonical analyses of peptide aggregation processes

We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterization of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.     

Microcanonical Phase Diagram of the BEG and Ising Models

The density of states of long-range Blume-Emery-Griffiths (BEG) and short-range Ising models are obtained by using Wang-Landau sampling with adaptive windows in energy and magnetization space. With accurate density of states, we are able to calculate the microcanonical specific heat of fixed magnetization introduced by Kastner et al. in the regions of positive and negative temperature. The microcanonical phase diagram of the Ising model shows a continuous phase transition at a negative temperature in energy and magnetization plane. However the phase diagram of the long-range model constructed by peaks of the microcanonical specific heat looks obviously different from the Ising chart.     

Microcanonical Phase Diagram of the BEG and Ising Models

The density of states of long-range Blume-Emery-Griffiths(BEG) and short-range Ising models are obtained by using Wang-Landau sampling with adaptive windows in energy and magnetization space.With accurate density of states,we are able to calculate the microcanonical specific heat of fixed magnetization introduced by Kastner et al.in the regions of positive and negative temperature.The microcanonical phase diagram of the Ising model shows a continuous phase transition at a negative temperature in energy and magnetization plane.However the phase diagram of the long-range model constructed by peaks of the microcanonical specific heat looks obviously different from the Ising chart.     

Negative heat capacity for a cluster of 147 sodium atoms

There exists a surprising theoretical prediction for a small system: its microcanonical heat capacity can become negative. An increase of energy can-under certain conditions-lead to a lower temperature. Here we present experimental evidence that a cluster containing exactly 147 sodium atoms does indeed have a negative microcanonical heat capacity near its solid to liquid transition.     

Phase transitions in small systems: Microcanonical vs. canonical ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.     

Ensemble inequivalence in random graphs

We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in a non-concave entropy function. The analytical solution is confirmed with numerical Metropolis and Creutz simulations and our results clearly demonstrate the presence of a region with negative specific heat and, consequently, ensemble inequivalence between the canonical and microcanonical ensembles.     

Equilibrium and ergodicity in small spin systems

The rearrangement of initial magnetic polarizations in a small isolated spin system does not lead to a uniform distribution as required by the microcanonical ensemble, but to a distribution of intermediate entropy as required by the initial conditions and auxiliary constants of the motion. The final equilibriumstate and the time to reach it are defined uniquely because of the finite number of discrete quantum states in such a system. Is such a system ergodic?     

Classification of Phase Transitions and Ensemble Inequivalence, in Systems with Long Range Interactions

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific heats and other non-common behaviors. We propose a classification of microcanonical phase transitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence. We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensional fluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet been observed in such systems.     

The equivalence of ensembles and the Gibbs phase rule for classical lattice systems

We study the relation between the microcanonical, canonical, and grand canonical ensembles in the thermodynamic limit when the system becomes infinite. They are equivalent if there is only one phase in the system. In general it is shown that there is a unique limit of the microcanonical state being a mixture of pure phases if the microcanonical restrictions determine the volume fractions of the phases uniquely, and then the Gibbs phase rule is valid. In this context we show how to define the set of order parameters associated with the state of the system in a natural way.     

Thermodynamics of the HMF model with a magnetic field

We study the thermodynamics of the Hamiltonian mean field (HMF) model with an external potential playing the role of a “magnetic field”. If we consider only fully stable states, the caloric curve does not present any phase transition. However, if we take into account metastable states (for a restricted class of perturbations), we find a very rich phenomenology. In particular, the caloric curve displays a region of negative specific heat in the microcanonical ensemble in which the temperature decreases as the energy increases. This leads to ensembles inequivalence and to zeroth order phase transitions similar to the “gravothermal catastrophe” and to the “isothermal collapse” of self-gravitating systems. In the present case, they correspond to the reorganization of the system from an “anti-aligned” phase (magnetization pointing in the direction opposite to the magnetic field) to an “aligned” phase (magnetization pointing in the same direction as the magnetic field). We also find that the magnetic susceptibility can be negative in the microcanonical ensemble so that the magnetization decreases as the magnetic field increases. The magnetic curves can take various shapes depending on the values of energy or temperature. We describe first order phase transitions and hysteretic cycles involving positive or negative susceptibilities. We also show that this model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking.     

Direct experimental evidence for a negative heat capacity in the liquid-to-gas phase transition in hydrogen cluster ions: backbending of the caloric curve

By selecting specific decay reactions in high-energy collisions (60 keV/amu) of hydrogen cluster ions with a helium target (utilizing event-by-event data of a recently developed multicoincidence experiment) and by deriving corresponding temperatures for these microcanonical cluster ensembles (analyzing respective fragment distributions), we are able to construct caloric curves for H+3(H2)(m) cluster ions (6相似文献   

Canonical typicality

It is well known that a system weakly coupled to a heat bath is described by the canonical ensemble when the composite S + B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schr?dinger in 1952.     

Microcanonical determination of the interface tension of flat and curved interfaces from Monte Carlo simulations

The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed and, as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q?=?30) on L?×?L square lattices (40?≤?L?≤?100) are presented. It is shown that the microcanonical ensemble is well suited both to find the precise location of the first-order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heat bath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature versus energy density is discussed, emphasizing that the extrema do not have the meaning of van der Waals-like 'spinodal points' separating metastable from unstable states, but rather describe the onset of heterophase states: droplet/bubble evaporation/condensation transitions. Thus all parts of these loops, including the parts that correspond to a negative specific heat, describe phase coexistence in full thermal equilibrium. However, the estimates for the curvature-dependent interface tension of the droplets and bubbles suffer from unexpected and unexplained large finite size effects which need further study.     

铜、银和铂原子纳米团簇负热容现象的分子动力学模拟研究

本文采用微正则分子动力学方法模拟研究了铂、铜和银原子纳米团族从固态到液态的熔化过程,得到热容量随温度变化关系,结果表明这三种金属纳米团簇在熔化过程中均出现了负热容现象,并通过对团簇热能随温度的变化关系以及团簇原子数径向分布的分析,探讨了产生负热容现象的微观机制.     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.