Condensed Matter

A study of the one-dimensional molecular chain (MC) with two single-particle degenerate states is presented. We establish connection of the MC with the Ising model with phononic interactions and investigate properties of the model using a transfer matrix method. The transfer matrix method offers a promising pathway for simulating such materials properties. The role of degeneracy of states and phononic interaction being made explicit. We analyze regimes of the system and parameters of the occurring crossover. Here, we present exact results for the magnetization per spin, the correlation function and the effective volume of the system. We demonstrate possibility of existence of two peaks in the specific heat capacity thermal behavior.

In this paper, we describe the diffusive and interconversion properties of a symmetric mixture of two different dynamics, characteristic for conserved and non-conserved order parameters, in the presence or absence of an external "source" of interconversion. We show that the interactions of the two competing dynamics of the order parameter (diffusion and interconversion) results in the phenomenon of "phase amplification," when one phase grows at the expense of another one. This phenomenon occurs when the order parameter exhibits even a small probability of non-conserved dynamics, thus breaking the particle conservation law. Also, we show that the addition of a source of interconversion drives the system away from equilibrium and creates the possibility for arrested phase separation - the existence of non-growing (steady-state) mesoscopic phase domains. These steady-state phase domains are an example of a simple dissipative structure. The change of the dynamics from phase amplification to microphase separation can be considered as a nonequilibrium "phase transition" in the dissipative system. The theoretical description is used to describe phase transitions affected by interconversion of an equilibrium and nonequilibrium lattice model.

We extend and successfully apply a recently proposed microstate nonequilibrium thermodynamics to study expansion/contraction processes. Here, the numbers of initial and final microstates are different so they cannot be connected by unique Hamiltonian trajectories. This commonly happens when the phase space volume changes, and has not been studied so far using Hamiltonian trajectories that can be inverted to yield an identity mapping between initial and final microstates as the parameter in the Hamiltonian is changed. We propose a trick to overcome this hurdle with a focus on free expansion in an isolated system, where the concept of dissipated work is not clear. The trick is shown to be thermodynamically consistent and can be extremely useful in simulation. We justify that it is the thermodynamic average of the internal microwork done by a microstate that is dissipated; this microwork is different from the exchange microwork with the vacuum, which vanishes. We also establish that the microwork is nonnegative for free expansion, which is remarkable, since its sign is not fixed in a general process.

Here, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine magnetisation, and the results of the derivation are interpreted graphically, physically, and mathematically. We give an interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

We propose a phase prediction method for the pattern formation in the uniaxial two-dimensional kinetic Ising model with the dipole-dipole interactions under the time-dependent Ginzburg-Landau dynamics. Taking the effects of the material thickness into account by assuming the uniformness along the magnetization axis, the model corresponds to thin magnetic materials with long-range repulsive interactions. We propose a new theoretical basis to understand the effects of the material parameters on the formation of the magnetic domain patterns in terms of the equation of balance governing the balance between the linear- and nonlinear forces in the equilibrium state. Based on this theoretical basis, we propose a new method to predict the phase in the equilibrium state reached after the time-evolution under the dynamics with a given set of parameters, by approximating the third-order term using the restricted phase-space approximation [R. Anzaki, K. Fukushima, Y. Hidaka, and T. Oka, Ann. Phys. 353, 107 (2015)] for the ϕ 4 -models. Although the proposed method does not have the perfect concordance with the actual numerical results, it has no arbitrary parameters and functions to tune the prediction. In other words, it is a method with no a priori assumptions on domain patterns.

We discuss a paradox from the field of relativistic thermodynamics: Two heat reservoirs of the same proper temperature move against each other. One is at rest in reference frame SA, the other in reference frame SB. For an observer, no matter in which of the two reference frames he is at rest, the temperatures of the two reservoirs are different. One might therefore conclude that a thermal engine can be operated between the reservoirs. However, the observers in SA and SB do not agree upon the direction of the entropy flow: from SA to SB, or from SB to SA. The resolution of the paradox is obtained by taking into account that the drive of an entropy current is not simply a temperature difference, but the difference of a quantity that depends on temperature and on velocity.

A mathematical model is presented for the dynamics of time relative to space. The model design is analogous to a chemical kinetic reaction based on transition state theory which posits the existence of reactants, activated complex, and products. Here, time future is considered to be analogous to reactants, time now to transition state (activated complex) and time past to products. Thus, future, now, and past events are considered to be distinct from one another in the progression of time which flows from future to now to past. The model also incorporates a cyclical reaction (in a quasi-equilibrium state) between time future and time now as well as an irreversible reaction (that is unidirectional and not in equilibrium) from time now to time past. The results from modeling show that modeling time in terms of changes in space can explain the asymmetric nature of time.

Memory effects in time-series of experimental observables are ubiquitous, have important cosequences for the interpretation of kinetic data, and may even affect the function of biomolecular nanomachines such as enzymes. Here we propose a set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate. The toolbox is general, robust, easy to use, and does not rely on any underlying microscopic model. As a proof of concept we apply it to the analysis of memory in the dynamics of the end-to-end distance of the analytically solvable Rouse-polymer model, an experimental time-series of extensions of a single DNA hairpin measured by optical tweezers, and the fraction of native contacts in a small protein probed by atomistic Molecular Dynamics simulations.

For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first-passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and non-reactive molecular states, which results in effective gating of product formation and altered reaction kinetics. To better understand this phenomenon we develop a unifying approach to gated reactions on networks. We first show that the mean and distribution of the gated reaction time can always be expressed in terms of ungated first-passage and return times. This relation between gated and ungated kinetics is then explored to reveal universal features of gated reactions. The latter are exemplified using a diverse set of case studies which are also used to expose the exotic kinetics that arises due to molecular gating.

A family of equilibria corresponding to dislocation-dipole, with variable separation between the two dislocations of opposite sign, is constructed in a one dimensional lattice model. A suitable path connecting certain members of this family is found which exhibits the familiar Peierls relief. A landscape for the variation of energy has been presented to highlight certain sequential transition between these equilibria that allows an interpretation in terms of quasi-statically separating pair of dislocations of opposite sign from the viewpoint of closely related Frenkel-Kontorova model. Closed form expressions are provided for the case of a piecewise-quadratic potential wherein an analysis of the effect of an intermediate spinodal region is included.