Continuous phase transitions with a convex dip in the microcanonical entropy

Behrinǵer, Hans; Pleimling, Michel

doi:10.1103/physreve.74.011108

Cited by 46 publications

(40 citation statements)

References 66 publications

(118 reference statements)

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“…The plots reveal an exciting phenomenon: Increasing the energy entails a reduction of temperature in the transition region, known as the backbending effect [3]. This signals a phaseseparation process [1,2] which is caused by surface effects reducing the entropy which, in an isolated system, results in a decrease of temperature by increasing the total system energy [3,4,[12][13][14][15]. This phenomenon is called "backbending effect", because the caloric temperature curve changes in the transition region its monotonic behavior with increasing total energy [3].…”

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confidence: 99%

Statistical mechanics of aggregation and crystallization for semiflexible polymers

2009

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Abstract. -By means of multicanonical computer simulations, we investigate thermodynamic properties of the aggregation of interacting semiflexible polymers. We analyze a mesoscopic beadstick model, where nonbonded monomers interact via Lennard-Jones forces. Aggregation turns out to be a process, in which the constituents experience strong structural fluctuations, similar to peptides in coupled folding-binding cluster formation processes. In contrast to a recently studied related proteinlike hydrophobic-polar heteropolymer model, aggregation and crystallization are separate processes for a homopolymer with the same small bending rigidity. Rather stiff semiflexible polymers form a liquid-crystal-like phase, as expected. In analogy to the heteropolymer study, we find that the first-order-like aggregation transition of the complexes is accompanied by strong system-size dependent hierarchical surface effects. In consequence, the polymer aggregation is a phase-separation process with entropy reduction.Cluster formation and crystallization of polymers are processes which are interesting for technological applications, e.g., for the design of new materials with certain mechanical properties or nanoelectronic organic devices and polymeric solar cells. From a biophysical point of view, the understanding of peptide oligomerization, but also the (de)fragmentation in semiflexible biopolymer systems like actin networks is of substantial relevance. This requires a systematic analysis of the basic properties of the polymeric cluster formation processes, in particular, for small polymer complexes on the nanoscale, where surface effects are competing noticeably with structure-formation processes in the interior of the aggregate.A further motivation for investigating the aggregation transition of semiflexible homopolymer chains derives from the intriguing results of our recent study of a similar aggregation process for peptides [1,2], which were modeled as heteropolymers with a sequence of two types of monomers, hydrophobic (A) and hydrophilic ones (B). By (a) E-mail: junghans@mpip-mainz.mpg.de (b) E-mail: m.bachmann@fz-juelich.de (c) E-mail: Wolfhard.Janke@itp.uni-leipzig.de specializing the previously employed heteropolymer model to the apparently simpler homopolymer case, we aim by comparison at isolating those properties which are mainly driven by the sequence properties of heteropolymers. In fact, while in both cases the aggregation transition is a phase-separation process, we will show below that for homopolymers the aggregation and crystallization (if any) are separate conformational transitions -unlike our study of heteropolymer aggregates where they were found to coincide [1,2]. The physical origin causing these differences will be explained within the microcanonical formalism [3,4], which proves [1,2] to be particularly suitable for this type of problem.We thus consider the same model as in [1,2], but here we assume that all monomers i µ = 1, . . . , N p-1

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confidence: 99%

Statistical mechanics of aggregation and crystallization for semiflexible polymers

2009

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“…In contrast to the backbending in the microcanonical caloric curve, T S ͑E͒, the inverse of the internal energy, T = U −1 ͑E͒, which corresponds to a caloric curve in the canonical ensemble, monotonically increases across the phase transition region, implying that statistical ensembles are not equivalent in finite size systems. 29 …”

Section: Scaling Behavior Of E and T S "E…mentioning

confidence: 99%

“…In many finite size systems, such as spins, 29 nuclei fragmentations, 30,31 model proteins, [32][33][34] and atomic clusters, 8,35,36 S͑E͒ shows a convex dip, i.e., ‫ץ‬ 2 S / ‫ץ‬E 2 Ͼ 0, 30 across the transition region, as sketched in Fig. 1͑a͒.…”

Section: Introductionmentioning

confidence: 99%

Generalized Replica Exchange Method

Kim

Keyes

Straub

2010

The Journal of Chemical Physics

109

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We present a powerful replica exchange method, particularly suited to first-order phase transitions associated with the backbending in the statistical temperature, by merging an optimally designed generalized ensemble sampling with replica exchanges. The key ingredients of our method are parametrized effective sampling weights, smoothly joining ordered and disordered phases with a succession of unimodal energy distributions by transforming unstable or metastable energy states of canonical ensembles into stable ones. The inverse mapping between the sampling weight and the effective temperature provides a systematic way to design the effective sampling weights and determine a dynamic range of relevant parameters. Illustrative simulations on Potts spins with varying system size and simulation conditions demonstrate a comprehensive sampling for phase-coexistent states with a dramatic acceleration of tunneling transitions. A significant improvement over the power-law slowing down of mean tunneling times with increasing system size is obtained, and the underlying mechanism for accelerated tunneling is discussed.

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“…The recent interest in the micro-canonical ensemble [1][2][3][4][5][6][7][8][9][10][11][12][13] is driven by the awareness that this ensemble is the cornerstone of statistical mechanics. Phase transitions described in the canonical ensemble could be linked to topological singularities of the micro-canonical energy landscape [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

On the Thermodynamics of Classical Micro-Canonical Systems

Baeten

Naudts

2011

Entropy

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We give two arguments why the thermodynamic entropy of non-extensive systems involves Rényi's entropy function rather than that of Tsallis. The first argument is that the temperature of the configurational subsystem of a mono-atomic gas is equal to that of the kinetic subsystem. The second argument is that the instability of the pendulum, which occurs for energies close to the rotation threshold, is correctly reproduced.

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Continuous phase transitions with a convex dip in the microcanonical entropy

Cited by 46 publications

References 66 publications

Statistical mechanics of aggregation and crystallization for semiflexible polymers

Statistical mechanics of aggregation and crystallization for semiflexible polymers

Generalized Replica Exchange Method

On the Thermodynamics of Classical Micro-Canonical Systems

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