In order to better understand the occurrence of phase transitions, we adopt an approach based on the study of energy landscapes: The relation between stationary points of the potential energy landscape of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied for finite as well as infinite systems. For finite systems, each stationary point is found to cause a nonanalyticity in the microcanonical entropy, and the functional form of this nonanalytic term can be derived explicitly. With increasing system size, the order of the nonanalytic term grows unboundedly, leading to an increasing differentiability of the entropy. Therefore, in the thermodynamic limit, only asymptotically flat stationary points may cause a phase transition to take place. For several spin models, these results are illustrated by predicting the absence or presence of a phase transition from stationary points and their local curvatures in microscopic configuration space. These results establish a relationship between properties of energy landscapes and the occurrence of phase transitions. Such an approach appears particularly promising for the simultaneous study of dynamical and thermodynamical properties, as is of interest for example for protein folding or the glass transition.
Kinetically constrained models (KCM) generically have trivial thermodynamics and yet manifest rich glassy dynamics. In order to resolve the thermodynamics-dynamics disconnect in KCMs, we derive a KCM by coarse-graining a non-trivial thermodynamic model with a solvable partition function. Blending of thermodynamics to the KCM makes the role of landscape properties on the relaxation times, fragility and its crossover analytically transparent. Using Bethe ansatz, we calculate the time-dependent $N$-point probability function in the distinct dynamical regimes of the landscapes; the contribution of…
Energy landscapes, ideal glasses, and their equation of state
利用Stillinger和Weber [Phys. Rev. A 25，978（1982）]最初提出的固有结构形式主义，我们概括了具有理想玻璃化转变的能量景观的热力学，并推导出其状态方程的结果。在这样做的过程中，我们确定了一个分离的结构和振动的贡献的压力，相应的模拟研究中进行的固有结构形式主义。我们开发了一个基本模型的景观适合简单的液体，这是基于软球势的标度特性的补充与平均场的吸引力。由此产生的状态方程提供了一个准确的表示模拟数据的Lennard-Jones流体，表明有用的基于水的配方的过冷液体热力学。最后，我们考虑的影响，一般理论和模型相对于所谓的Sastry密度和理想的玻璃化转变。我们的分析表明，定量之间的联系，可以作出的景观和模拟确定的Sastry密度的属性，它强调了理想的玻璃化转变和Kauzmann等熵条件之间的区别。
A Potts model and the Replica Exchange Wang-Landau algorithm are used to construct an energy landscape for a crystalline solid containing surfaces and grain boundaries. The energy landscape is applied to an equation of motion from the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework to explore the kinetics of three distinct kinds of microstructural evolution: polycrystalline sintering, precipitate coarsening, and grain growth. The steepest entropy ascent postulate predicts unique kinetic paths for these non-equilibrium processes without needing any detailed information about the…
We present the study of the landscape structure of athermal soft spheres both as a function of the packing fraction and of the energy. We find that, on approaching the jamming transition, the number of different configurations available to the system has a steep increase and that a hierarchical organization of the landscape emerges. We use the knowledge of the structure of the landscape to predict the values of thermodynamic observables on the edge of the transition.
Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models - based on the assumption of the existence of two types of competing local states (or, structures) in liquid water - have been extremely successful in describing water's thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a geometrical order parameter-free approach to unambiguously identify the two types of competing local states -- entropically and energet…
Discrete-time counterpart of thermodynamic uncertainty relation (conjectured in P. Pietzonka, et.al., arXiv:1702.07699 (2017)) with finite time interval is considered. We show that this relation do not hold by constructing a concrete counterexample to this. Our finding suggests that the proof of thermodynamic uncertainty relation with finite time interval, if true, should strongly rely on the fact that the time is continuous.
An extension of the thermodynamic uncertainty relation (TUR) to time-delayed Langevin systems has been recently proposed by T. V. Vu and Y. Hasegawa (arXiv:1809.06610v2). Here we show that the derivation is erroneous.
In recent letter [Phys.~Rev.~Lett {\bf 123}, 110602 (2019)], Y.~Hasegawa and T.~V.~Vu derived a thermodynamic uncertainty relation. But the bound of their relation is loose. In this comment, through minor changes, an improved bound is obtained. This improved bound is the same as the one obtained in [Phys.~Rev.~Lett {\bf 123}, 090604 (2019)] by A.~M.~Timpanaro {\it et. al.}, but the derivation here is straightforward.
The nonextensive thermodynamic relations are expressed under the assumption of temperature duality, endowing the "physical temperature" and the "Lagrange temperature" in different physical sense. Based on this assumption, two sets of parallel Legendre transform structures are given. One is called "physical" set, and the other called "Lagrange" set. In these two formalisms, the thermodynamic quantities and the thermodynamic relations are both liked through the Tsallis factor. Application of the two sets of the thermodynamic relations to the self-gravitating system shows that the heat capacity d…
We generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems (Gingrich et al., Phys. Rev. Lett. 116, 120601 (2016)), to time-discrete Markov chains and to systems under time-symmetric, periodic driving.
The thermodynamic uncertainty relations provide a universal trade-offs between entropy dissipation rate and fluctuations in transport current. This relation has been mostly used to estimate a minimum entropy dissipation rate by experimentally measuring current fluctuations. Here we consider joint currents and show that such uncertainty relations cannot be simultaneously achievable for any two currents, which leads to a potential underestimation of the minimum entropy dissipation rate.
Thermal fluctuations can lift the degeneracy of a ground state manifold, producing a free energy landscape without accidentally degenerate minima. In a process known as order by disorder, a subset of states incorporating symmetry-breaking may be selected. Here, we show that such a free energy landscape can be controlled in a non-equilibrium setting as the slow motion within the ground state manifold is governed by the fast modes out of it. For the paradigmatic case of the classical pyrochlore XY antiferromagnet, we show that a uniform magnetic field pulse can excite these fast modes to generat…
We introduce a model for a periodically driven electron pump that sequentially interact with an arbitrary number of heat and particle reservoirs. Exact expressions for the thermodynamic fluxes, such as entropy production and particle flows are derived arbitrarily far from equilibrium. We use the present model to perform a comparative study of thermodynamic uncertainty relations that are valid for systems with time-periodic driving.
The fluctuation-dissipation-theorem connects equilibrium to mildly (linearly) perturbed situations in a thermodynamic manner: It involves the observable of interest and the entropy production caused by the perturbation. We derive a relation which connects responses of arbitrary order in perturbation strength to correlations of entropy production of lower order, thereby extending the fluctuation-dissipation-theorem to cases far from equilibrium in a thermodynamic way. The relation is validated and studied for a 4-state-model.
The thermodynamic uncertainty relation expresses a seemingly universal trade-off between the cost for driving an autonomous system and precision in any output observable. It has so far been proven for discrete systems and for overdamped Brownian motion. Its validity for the more general class of underdamped Brownian motion, where inertia is relevant, was conjectured based on numerical evidence. We now disprove this conjecture by constructing a counterexample. Its design is inspired by a classical pendulum clock, which uses an escapement to couple the motion of an oscillator to another degree o…
The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a recently conjectured finite-time thermodynamic uncertainty relation for steady-state current fluctuations. Our proof is based on a quadratic bound to the large deviation rate function for currents in the limit of a large ensemble of many copies.
We demonstrate that the Einstein relation for the diffusion of a particle in the random energy landscape with the Gaussian density of states is an exclusive 1D property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish connection between these properties and dimensionality and spatial correlation of the random energy landscape.
