Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter

We analyze thermodynamic bounds on equilibrium fluctuations of an order parameter, which are analogous to relations, which have been derived recently in the context of non-equilibrium fluctuations of currents. We discuss the case of {\it global} fluctuations when the order parameter is measured in the full system of interest, and {\it local} fluctuations, when the order parameter is evaluated only in a sub-part of the system. Using isometric fluctuation theorems, we derive thermodynamic bounds on the fluctuations of the order parameter in both cases. These bounds could be used to infer the value of symmetry breaking field or the relative size of the observed sub-system to the full system from {\it local} fluctuations.Comment: 8 pages, 6 figures, in press for Europhys. Let

Isometric fluctuation relations for equilibrium states with broken symmetry

We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to many condensed-matter physics systems. Here, we establish these relations for magnetic systems and nematic liquid crystals in a symmetry-breaking external field, and we illustrate them on the Curie-Weiss and the $XY$ models. Our relations also have implications for spontaneous symmetry breaking, which are discussed.Comment: 9 pages, 4 figures, in press for Phys. Rev. Lett. to appear there in Dec. 201

A Poisson-Boltzmann approach for a lipid membrane in an electric field

The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (DC) electric field is investigated theoretically in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli which are analyzed here. We show that, especially in the low salt limit, i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime. ii) the contribution to the membrane's bending modulus due to the Debye layers saturates for high voltages. Nevertheless, the membrane undulation instability due to an effectively negative surface tension as predicted by linear Debye-H\"uckel theory is shown to persist in the nonlinear, high voltage regime.Comment: 15 pages, 4 figure

Phase transitions in optimal strategies for betting

Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk free strategy.Comment: 23 pages, 5 figure

Stokes parameters for light scattering from a Faraday-active sphere

We present an exact calculation for the scattering of light from a single sphere made of Faraday-active material, to first order in the external magnetic field. We use a recent expression for the T-matrix of a Mie scatterer in a magnetic field to compute the Stokes parameters in single scattering that describe completely flux and polarization of the scattered light.Comment: 17 pages, 5 figures, Latex, accepted for publication in JQSR

Thermal expansion within a chain of magnetic colloidal particles

We study the thermal expansion of chains formed by self-assembly of magnetic colloidal particles in a magnetic field. Using video-microscopy, complete positional data of all the particles of the chains is obtained. By changing the ionic strength of the solution and the applied magnetic field, the interaction potential can be tuned. We analyze the thermal expansion of the chain using a simple model of a one dimensional anharmonic crystal of finite size.Comment: 5 pages and 3 figure