Equilibrium fluctuation theorems compatible with anomalous response

Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations $C=\beta^{2}<\delta U^{2}>$, which is able to describe the existence of macrostates with negative heat capacities $C<0$. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the \textit{fundamental and the complementary fluctuation theorems}, which represent the generalization of two fluctuation identities already obtained in previous works, and the \textit{associated fluctuation theorem}, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of 2D Ising model.Comment: Extended version of the paper published in JSTA

Polyimide adhesives

A process was developed for preparing aromatic polyamide acids for use as adhesives by reacting an aromatic dianhydride to an approximately equimolar amount of an aromatic diamine in a water or lower alkanol miscible ether solvent. The polyamide acids are converted to polyimides by heating to the temperature range of 200 - 300 C. The polyimides are thermally stable and insoluble in ethers and other organic solvents

Geometrical aspects and connections of the energy-temperature fluctuation relation

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The

Process for preparing polyimide adhesives

High bonding strengths are obtained for metals and fiber-reinforced organic resin composites with no significant loss in thermo-oxidative stability of the adhesive resin

Polyimide adhesives

A process of preparing aromatic polyamide-acids for use as adhesives is described. An equimolar quantity of an aromatic dianhydride is added to a stirred solution of an aromatic diamine in a water or alcohol-miscible ether solvent to obtain a viscous polymer solution. The polymeric-acid intermediate polymer does not become insoluble but directly forms a smooth viscous polymer solution. These polyamic-acid polymers are converted, by heating in the range of 200-300 C and with pressure, to form polyimides with excellent adhesive properties

Thermodynamic fluctuation relation for temperature and energy

The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $=1+< \delta {E^{2}}> \partial ^{2}S(E) /\partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.Comment: Version accepted for publication in J. Phys. A: Math and The

Models for quantitative charge imaging by atomic force microscopy

Two models are presented for quantitative charge imaging with an atomic-force microscope. The first is appropriate for noncontact mode and the second for intermittent contact (tapping) mode imaging. Different forms for the contact force are used to demonstrate that quantitative charge imaging is possible without precise knowledge of the contact interaction. From the models, estimates of the best charge sensitivity of an unbiased standard atomic-force microscope cantilever are found to be on the order of a few electrons

Self-Interacting Dark Matter Halos and the Gravothermal Catastrophe

We study the evolution of an isolated, spherical halo of self-interacting dark matter (SIDM) in the gravothermal fluid formalism. We show that the thermal relaxation time, $t_r$, of a SIDM halo with a central density and velocity dispersion of a typical dwarf galaxy is significantly shorter than its age. We find a self-similar solution for the evolution of a SIDM halo in the limit where the mean free path between collisions, $\lambda$, is everywhere longer than the gravitational scale height, $H$. Typical halos formed in this long mean free path regime relax to a quasistationary gravothermal density profile characterized by a nearly homogeneous core and a power-law halo where $\rho \propto r^{-2.19}$. We solve the more general time-dependent problem and show that the contracting core evolves to sufficiently high density that $\lambda$ inevitably becomes smaller than $H$ in the innermost region. The core undergoes secular collapse to a singular state (the ``gravothermal catastrophe'') in a time $t_{coll} \approx 290 t_r$, which is longer than the Hubble time for a typical dark matter-dominated galaxy core at the present epoch. Our model calculations are consistent with previous, more detailed, N-body simulations for SIDM, providing a simple physical interpretation of their results and extending them to higher spatial resolution and longer evolution times. At late times, mass loss from the contracting, dense inner core to the ambient halo is significantly moderated, so that the final mass of the inner core may be appreciable when it becomes relativistic and radially unstable to dynamical collapse to a black hole.Comment: ApJ in press (to appear in April), 12 pages. Extremely minor changes to agree with published versio

Electromagnetic Magic: The Relativistically Rotating Disk

A closed form analytic solution is found for the electromagnetic field of the charged uniformly rotating conducting disk for all values of the tip speed $v$ up to $c$. For $v=c$ it becomes the Magic field of the Kerr-Newman black hole with $G$ set to zero. The field energy, field angular momentum and gyromagnetic ratio are calculated and compared with those of the electron. A new mathematical expression that sums products of 3 Legendre functions each of a different argument, is demonstrated.Comment: 10 pages, one figur