The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. on topological signatures of the spherical model are elucidated. Phase transitions, like the boiling and evaporating of water at a certain temperature and pressure, are common phenomena both in everyday life and in almost any branch of physics. Loosely speaking, a phase transition brings about a sudden change of the macroscopic properties of a many-particle system while smoothly varying a parameter (the temperature or the pressure in the above example). The mathematical description of phase transitions is conventionally based on (grand)canonical thermodynamic functions, relating their loss of analyticity to the occurrence of a phase transition. Such a nonanalytic behavior in a (grand)canonical thermodynamic function can occur only in the thermodynamic limit in which the number of degrees of freedom N of the system goes to infinity [1].Many researchers took it for granted that the same were true also for microcanonical thermodynamic functions. Recently, however, it was observed that the microcanonical entropy, or Boltzmann entropy, of a finite system is not necessarily analytic, and nonanalytic entropy functions of finite systems have been reported for certain classical models [2,3,4].In light of their conceptual similarity to the definition of a phase transition, it is tempting to regard finitesystem nonanalyticities of the entropy as phase transitionlike phenomena. This point of view is advocated in [4], and the authors of that reference argue that such nonanalyticities should also be measurable experimentally, at least in very small systems. However, such an interpretation is complicated by the fact that, as discussed in [3], for typical models the number of nonanalytic points of the entropy increases unboundedly with the number of degrees of freedom N .Because of their typically large number, one might assume that nonanalyticities of the finite-system entropy were unrelated to the occurrence of a phase transition in the thermodynamic limit. A theorem by Franzosi and Pettini [5], however, indicates the existence of a relation between finite-system and infinite-system nonanalyticities (and we will come back to that theorem later). The purpose of the present Letter is to clarify and quantify the ...

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its Boltzmann entropy is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived for the generic case of potentials having the Morse property. With increasing system size the order of the nonanalytic term grows unboundedly, leading to an increasing differentiability of the entropy. Nonetheless, a distribution of an unboundedly growing number of saddle points may cause a phase transition in the thermodynamic limit. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, conditions on the distribution of saddle points and their curvatures are derived which are necessary for a phase transition to occur. With these results, the puzzling absence of topological signatures in the spherical model is elucidated. As further applications, the phase transitions of the mean-field XY model and the mean-field k-trigonometric model are shown to be induced by saddle points of vanishing curvature.

We study the conformational transition of an ensemble of magnetic particles from a linear chain to a compact cluster when subjected to an external magnetic field modulation. We show that the transient dynamics induced by switching the field from static to rotating is governed by the relative friction of adjacent particles in the chain. Solid particles show bending solitons counter-propagating along the chain while buckling of the chain is the mechanism preferred by ferrofluid droplets. By combining real-space experiments with numerical simulations we unveil the underlying mechanism of folding pathways in driven colloidal systems.

We present a numerical investigation of the Brownian motion and diffusion of a dumbbell in a two-dimensional periodic potential. Its dynamics is described by a Langevin model including the hydrodynamic interaction. With increasing values of the amplitude of the potential we find along the modulated spatial directions a reduction of the diffusion constant and of the impact of the hydrodynamic interaction. For modulation amplitudes of the potential in the range of the thermal energy the dumbbell diffusion exhibits a pronounced local maximum at a wavelength of about 3/2 of the dumbbell extension. This is especially emphasized for stiff springs connecting the two beads. Introduction.-Investigations on the diffusion of different colloidal particles in a homogeneous solvent have a long history [1,2], while studies on the diffusion of small spheres, dimers and polymers in different potentials attract considerable interest only for a short time [3,4,5,6,7,8,9]. Laser-tweezer arrays are a new powerful tool for generating the desired spatially periodic, correlated or unstructured potentials in order to study the effects of inhomogeneous potential landscapes on the motion of colloidal particles [3,4,5,10]. Furthermore recent studies of dumbbells and polymers in random potentials are exciting issues in statistical physics [11,12].

We have studied the interactions between magnetically driven, DNA-linked anisotropic and isotropic colloidal rotors interacting via induced magnetic dipolar and multipolar forces. We show that a balance between magnetic dipole-dipole and dipole-hexapole interactions near the magic angle allows discrimination between spherical and anisotropic magnetic colloidal rotors.