Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath

The standard textbooks contain good explanations of how and why equilibrium thermodynamics emerges in a reservoir with particles that are subjected to Gaussian noise. However, in systems that convert or transport energy, the noise is often not Gaussian. Instead, displacements exhibit an [Formula: see text]-stable distribution. Such noise is commonly called Lévy noise. With such noise, we see a thermodynamics that deviates from what traditional equilibrium theory stipulates. In addition, with particles that can propel themselves, so-called active particles, we find that the rules of equilibrium thermodynamics no longer apply. No general nonequilibrium thermodynamic theory is available and understanding is often ad hoc. We study a system with overdamped particles that are subjected to Lévy noise. We pick a system with a geometry that leads to concise formulae to describe the accumulation of particles in a cavity. The nonhomogeneous distribution of particles can be seen as a dissipative structure, i.e., a lower-entropy steady state that allows for throughput of energy and concurrent production of entropy. After the mechanism that maintains nonequilibrium is switched off, the relaxation back to homogeneity represents an increase in entropy and a decrease of free energy. For our setup we can analytically connect the nonequilibrium noise and active particle behavior to entropy decrease and energy buildup with simple and intuitive formulae

Application of graphene as a nanoindenter interacting with phospholipid membranes - computer simulation study

Synthesis of graphene (GN) in 2004 stimulated wide interest inpotential applications of 2D materials in catalysis, optoelectronics, biotechnology,and construction of sensing devices. In the presented study, interactions betweenGN sheets and phospholipid bilayers are examined using steered moleculardynamics simulations. GN sheets of different sizes were inserted into a bilayer andsubsequently withdrawn from it at two different rates (1 and 2 m/s). In somecases, nanoindentation led to substantial damage of the phospholipid bilayer;however, an effective self-sealing process occurred even after significantdegradation. The average force and work, deflection of the membrane duringindentation, withdrawal processes, and structural changes caused by moving sheetsare discussed. These quantities are utilized to estimate the suitability of GN sheetsfor targeted drug delivery or other nanomedicine tools. The results are comparedwith those obtained for other nanostructures such as homogeneous andheterogeneous nanotubes

Formation of Protein Networks between Mucins: Molecular Dynamics Study Based on the Interaction Energy of the System

Molecular dynamics simulations have been performed for a model aqueous solution of mucin. As mucin is a central part of lubricin, a key component of synovial fluid, we investigate its ability to form cross-linked networks. Such network formation could be of major importance for the viscoelastic properties of the soft-matter system and crucial for understanding the lubrication mechanism in articular cartilage. Thus, the inter- and intra-molecular interaction energies between the residues of mucin are analyzed. The results indicate that the mucin concentration significantly impacts its cross-linking behavior. Between 160 g/L and 214 g/L, there seems to be a critical concentration above which crowding begins to alter intermolecular interactions and their energies. This transition is further supported by the mean squared displacement of the molecules. At a high concentration, the system starts to behave subdiffusively due to network development. We also calculate a sample mean squared displacement and p-variation tests to demonstrate how the statistical nature of the dynamics is likewise altered for different concentrations

Steered molecular dynamics of lipid membrane indentation by carbon and silicon-carbide nanotubes - the impact of indenting angle uncertainty

Due to the semi-liquid nature and uneven morphologies of biological membranes, indentation may occur in a range of non-ideal conditions. These conditions are relatively unstudied and may alter the physical characteristics of the process. One of the basic challenges in the construction of nanoindenters is to appropriately align the nanotube tip and approach the membrane at a perpendicular angle. To investigate the impact of deviations from this ideal, we performed non-equilibrium steered molecular dynamics simulations of the indentation of phospholipid membranes by homogeneous CNT and non-homogeneous SiCNT indenters. We used various angles, rates, and modes of indentation, and the withdrawal of the relative indenter out of the membrane in corresponding conditions was simulated

Lèvy noise induced steady states

Systems far from equilibrium organize themselves to accommodate energy throughput. It is also in these nonequilibrium systems where noise has often been found to follow alpha-stable distributions, commonly called Lèvy noise, rather than Gaussian distributions. There is no general theory that links these alpha-stable distributions to the resultant thermodynamic behavior of a system as a whole. Here two different model systems are investigated for which the assumption of Lèvy noise leads to behavior that deviates from that seen at equilibrium. We begin by examining trajectories of overdamped noise-driven particles in a harmonic potential. These trajectories display broken time reversal symmetry due to the large displacements inherent to Lèvy noise. A parameter to measure this symmetry breaking and estimate the stability parameter, ɑ, of the underlying noise is proposed. This parameter is applied to a time series of solar x-ray irradiance and compared to previous methods. Next, we study the same overdamped particles in a 2D system with simple semi-circular cavities. Lèvy noise in such a system will lead to a preferential accumulation of particles in one cavity. The nonhomogeneous steady-state represents a lower entropy configuration in comparison to equilibrium. The chosen system leads to concise expressions for the distribution of particles within the cavities as well as the concomitant entropy reduction. Such structures maintained in nonequilibrium have been referred to as dissipative structures because they may aid the system in transporting or dissipating energy

Lèvy noise induced steady states

Systems far from equilibrium organize themselves to accommodate energy throughput. It is also in these nonequilibrium systems where noise has often been found to follow alpha-stable distributions, commonly called Lèvy noise, rather than Gaussian distributions. There is no general theory that links these alpha-stable distributions to the resultant thermodynamic behavior of a system as a whole. Here two different model systems are investigated for which the assumption of Lèvy noise leads to behavior that deviates from that seen at equilibrium. We begin by examining trajectories of overdamped noise-driven particles in a harmonic potential. These trajectories display broken time reversal symmetry due to the large displacements inherent to Lèvy noise. A parameter to measure this symmetry breaking and estimate the stability parameter, ɑ, of the underlying noise is proposed. This parameter is applied to a time series of solar x-ray irradiance and compared to previous methods. Next, we study the same overdamped particles in a 2D system with simple semi-circular cavities. Lèvy noise in such a system will lead to a preferential accumulation of particles in one cavity. The nonhomogeneous steady-state represents a lower entropy configuration in comparison to equilibrium. The chosen system leads to concise expressions for the distribution of particles within the cavities as well as the concomitant entropy reduction. Such structures maintained in nonequilibrium have been referred to as dissipative structures because they may aid the system in transporting or dissipating energy

How a Nonequilibrium Bath and a Potential Well Lead to Broken Time-Reversal Symmetry—First-Order Corrections on Fluctuation–Dissipation Relations

The noise that is associated with nonequilibrium processes commonly features more outliers and is therefore often taken to be Lévy noise. For a Langevin particle that is subjected to Lévy noise, the kicksizes are drawn not from a Gaussian distribution, but from an α-stable distribution. For a Gaussian-noise-subjected particle in a potential well, microscopic reversibility applies. However, it appears that the time-reversal-symmetry is broken for a Lévy-noise-subjected particle in a potential well. Major obstacles in the analysis of Langevin equations with Lévy noise are the lack of simple analytic formulae and the infinite variance of the α-stable distribution. We propose a measure for the violation of time-reversal symmetry, and we present a procedure in which this measure is central to a controlled imposing of time-reversal asymmetry. The procedure leads to behavior that mimics much of the effects of Lévy noise. Our imposing of such nonequilibrium leads to concise analytic formulae and does not yield any divergent variances. Most importantly, the theory leads to simple corrections on the Fluctuation–Dissipation Relation

How a Nonequilibrium Bath and a Potential Well Lead to Broken Time-Reversal Symmetry—First-Order Corrections on Fluctuation–Dissipation Relations

The noise that is associated with nonequilibrium processes commonly features more outliers and is therefore often taken to be Lévy noise. For a Langevin particle that is subjected to Lévy noise, the kicksizes are drawn not from a Gaussian distribution, but from an α-stable distribution. For a Gaussian-noise-subjected particle in a potential well, microscopic reversibility applies. However, it appears that the time-reversal-symmetry is broken for a Lévy-noise-subjected particle in a potential well. Major obstacles in the analysis of Langevin equations with Lévy noise are the lack of simple analytic formulae and the infinite variance of the α-stable distribution. We propose a measure for the violation of time-reversal symmetry, and we present a procedure in which this measure is central to a controlled imposing of time-reversal asymmetry. The procedure leads to behavior that mimics much of the effects of Lévy noise. Our imposing of such nonequilibrium leads to concise analytic formulae and does not yield any divergent variances. Most importantly, the theory leads to simple corrections on the Fluctuation–Dissipation Relation

Lèvy noise induced steady states

Systems far from equilibrium organize themselves to accommodate energy throughput. It is also in these nonequilibrium systems where noise has often been found to follow alpha-stable distributions, commonly called Lèvy noise, rather than Gaussian distributions. There is no general theory that links these alpha-stable distributions to the resultant thermodynamic behavior of a system as a whole. Here two different model systems are investigated for which the assumption of Lèvy noise leads to behavior that deviates from that seen at equilibrium. We begin by examining trajectories of overdamped noise-driven particles in a harmonic potential. These trajectories display broken time reversal symmetry due to the large displacements inherent to Lèvy noise. A parameter to measure this symmetry breaking and estimate the stability parameter, ?, of the underlying noise is proposed. This parameter is applied to a time series of solar x-ray irradiance and compared to previous methods.\n \n Next, we study the same overdamped particles in a 2D system with simple semi-circular cavities. Lèvy noise in such a system will lead to a preferential accumulation of particles in one cavity. The nonhomogeneous steady-state represents a lower entropy configuration in comparison to equilibrium. The chosen system leads to concise expressions for the distribution of particles within the cavities as well as the concomitant entropy reduction. Such structures maintained in nonequilibrium have been referred to as dissipative structures because they may aid the system in transporting or dissipating energy