Comparison of Boltzmann and Gibbs entropies for the analysis of single-chain phase transitions

Shakirov, Timur; Zablotskiy, Sergey V.; Böker, Arne; Иванов, В. А.; Paul, Wolfgang

doi:10.1140/epjst/e2016-60326-1

Cited by 12 publications

(18 citation statements)

References 40 publications

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“…For the semi-flexible chains (0.56≤L<1), a smeared out step is still there for L=0.56 but is smoothed out for larger L , while, at the same time, a maximum in the entropy occurs at finite energy. For energies larger than this value, the inverse micro-canonical temperature becomes negative, a well known behavior for the Boltzmann entropy of finite systems, which can be avoided by using the Gibbs definition of entropy [40,41].…”

Section: Resultsmentioning

confidence: 99%

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2017

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Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations-a type of flat-histogram Monte Carlo method-determining the density of states of a model class of single semi-flexible polymer chains, and, from this, their complete thermodynamic behavior. The chains possess a rich pseudo phase diagram as a function of stiffness and temperature, displaying non-trivial ground-state morphologies. This pseudo phase diagram also depends on chain length. Differences to existing pseudo phase diagrams of semi-flexible chains in the literature emphasize the fact that the mechanism of stiffness creation matters.

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Section: Resultsmentioning

confidence: 99%

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2017

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“…We divided the configuration space of microstates (conformations) into regions containing microstates for a particular “macrostate”, which we have defined by a pair of two energy terms (Env,nst) (assuming a given εst) and accumulated the two-Dimensional Density of States (2D DoS) function g(Env,nst). The 2D DoS function has essential advantages in comparison with the 1D DoS function, described and explained in [9,10,11,43,44,45], although it is much more time consuming in simulations. We used two types of trial Monte Carlo moves: a local displacement of a randomly-chosen monomer unit (uniformly in the interval [−0.05;0.05] along each axis) and an “end-cut-and-regrow” move [11].…”

Section: Model and Simulation Techniquesmentioning

confidence: 99%

Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2019

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The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length N = 64 with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the “conformational” microcanonical ( N V U , where U is the potential energy) and the true microcanonical ( N V E , where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature.

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“…For instance, classical spin systems where the kinetic energy is usually not defined in the Hamiltonian. However, here we are concerned with the "real" microcanonical ensemble wherein the kinetic energy part is also considered [26,27]. The integration over the momentum variables can be performed analytically in (4) and leads to…”

Section: A Microcanonical Ensemblementioning

confidence: 99%

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

Kumar

Chandramouli

et al. 2018

Phys. Rev. E

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We consider a class of systems where N identical particles with positions q1, ..., qN and momenta p1, ..., pN are enclosed in a box of size L, and exhibit the scaling U(Lr1, ..., LrN ) = α(L) U(r1, ..., rN ) for the associated potential energy function U(q1, ..., qN ). For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description, and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach, as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box. arXiv:1810.11623v2 [cond-mat.stat-mech]

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Comparison of Boltzmann and Gibbs entropies for the analysis of single-chain phase transitions

Cited by 12 publications

References 40 publications

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

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