Subphase transitions in first-order aggregation processes

Koci, Tomas; Bachmann, Michael

doi:10.1103/physreve.95.032502

Cited by 9 publications

(5 citation statements)

References 71 publications

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“…In this context, it has been common to analyze first-order-like transitions in finite systems by means of Maxwell's construction, where the backbending region in the transition regime of the energetic temperature curve is replaced by a flat segment. However, Maxwell construction only applies to single transitions of first order and can neither be used if the transition is composed or accompanied by subphase transitions [10], nor if it is of higher order. However, by replacing the "flatness" idea of Maxwell's construction by the more general principle of minimal sensitivity [11], these issues can be resolved as will be discussed in the following.…”

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confidence: 99%

Classification of Phase Transitions by Microcanonical Inflection-Point Analysis

Bachmann

2018

Phys. Rev. Lett.

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By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of systematically identifying and locating independent and dependent phase transitions of any order is proposed. The power of the generalized method is demonstrated in applications to the ferromagnetic Ising model and a coarse-grained model for polymer adsorption onto a substrate. The results shed new light on the intrinsic phase structure of systems with cooperative behavior.

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confidence: 99%

Classification of Phase Transitions by Microcanonical Inflection-Point Analysis

Bachmann

2018

Phys. Rev. Lett.

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“…A different classification, known as microcanonical analysis, has been proposed by Gross [2,3] and it identifies PTs with the presence of convex region of microcanonical entropy. Recently, Bachmann et al [4][5][6][7][8][9][10] developed a novel classification of PTs called microcanonical inflection-point analysis. The signature of a PT is represented by a least-sensitive inflection point in the derivatives of the microcanonical entropy distinguishing between independent and dependent PTs.…”

Section: Introductionmentioning

confidence: 99%

The geometric theory of phase transitions

Cairano¹

2022

J. Phys. A: Math. Theor.

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We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. Such a theory allows to rephrase the Bachmann's classification of PTs for finite-size systems in terms of geometric properties of the energy level sets (ELSs) associated to the Hamiltonian function. Specifically, by defining the microcanonical entropy as the logarithm of the ELS’s volume equipped with a suitable metric tensor, we obtain an exact equivalence between thermodynamics and geometry. In fact, we show that any energy-derivative of the entropy can be associated to a specific combination of geometric curvature structures of the ELSs which, in turn, are well-precise combinations of the potential function derivatives. In so doing, we establish a direct connection between the microscopic description provided by the Hamiltonian and the collective behavior which emerges in a PT. Finally, we also analyze the behavior of the ELSs' geometry in the thermodynamic limit showing that nonanalyticities of the energy-derivatives of the entropy are caused by nonanalyticities of certain geometric properties of the ELSs around the transition point. We validate the theory studying the PTs that occur in the $\phi^4$ and Ginzburg-Landau-like models.

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“…Examples of computational studies include not only lattice [17][18][19][20][21][22][23][24] and magnetic models 25,26 , but also more sophisticated biopolymeric systems, in particular, models for peptide aggregation [27][28][29][30][31][32][33] , protein dimerization 34 , homopolymer collapse [35][36][37] , protein folding [38][39][40][41][42][43][44][45][46][47][48] , and polymer adsorption [49][50][51] .…”

Section: Introductionmentioning

confidence: 99%

Microcanonical characterization of first-order phase transitions in a generalized model for aggregation

Trugilho,

Rizzi

2021

Preprint

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Aggregation transitions in disordered mesoscopic systems play an important role in several areas of knowledge, from materials science to biology. The lack of a thermodynamic limit in systems that are intrinsically finite makes the microcanonical thermostatistics analysis, which is based on the microcanonical entropy, a suitable alternative to study the aggregation phenomena. Although microcanonical entropies have been used in the characterization of first-order phase transitions in many nonadditive systems, most of the studies are only done numerically with aid of advanced Monte Carlo simulations. Here we consider a semi-analytical approach to characterize aggregation transitions that occur in a generalized model related to the model introduced by Thirring. By considering an effective interaction energy between the particles in the aggregate, our approach allowed us to obtain scaling relations not only for the microcanonical entropies and temperatures, but also for the sizes of the aggregates and free-energy profiles. In addition, we test the approach commonly used in simulations which is based on the conformational microcanonical entropy determined from a density of states that is a function of the potential energy only. Besides the evaluation of temperature versus concentration phase diagrams, we explore this generalized model to illustrate how one can use the microcanonical thermostatistics as an analysis method to determine experimentally relevant quantities such as latent heats and free-energy barriers of aggregation transitions.

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Subphase transitions in first-order aggregation processes

Cited by 9 publications

References 71 publications

Classification of Phase Transitions by Microcanonical Inflection-Point Analysis

Classification of Phase Transitions by Microcanonical Inflection-Point Analysis

The geometric theory of phase transitions

Microcanonical characterization of first-order phase transitions in a generalized model for aggregation

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