The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures

Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical mechanics especially its key quantity, entropy. Whereas in conventional thermostatistics, the homogeneity and extensivity of the system and the concavity of its entropy are central conditions, these fail for the systems considered here. For example, at phase separation, the entropy, S(E), is necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as inhomogeneities and surface effects cannot be scaled away, one must be careful with the standard arguments of splitting a system into two subsystems, or bringing two systems into thermal contact with energy or particle exchange. Not only the volume part of the entropy must be considered. As will be shown here, when removing constraints in regions of a negative heat capacity, the system may even relax under a flow of heat (energy) against a temperature slope. Thus the Clausius formulation of the second law: ``Heat always flows from hot to cold'', can be violated. Temperature is not a necessary or fundamental control parameter of thermostatistics. However, the second law is still satisfied and the total Boltzmann entropy increases. In the final sections of this paper, the general microscopic mechanism leading to condensation and to the convexity of the microcanonical entropy at phase separation is sketched. Also the microscopic conditions for the existence (or non-existence) of a critical end-point of the phase-separation are discussed. This is explained for the liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of Chemical Physic

INDICATION OF META-ANTHRACITE BY MAGNETOTELLURICS IN THE KŐSZEG-RECHNITZ PENNINIC WINDOW : A TEST AREA

One of the Penninic Nappes is the Kőszeg-Rechnitz (K-R) tectonic window at the Eastern end of the Eastern Alps. It has a complicated metamorphic history from the Jurassic time. The organic material of the Penninic Ocean was transformed to electrically conductive meta-anthracite. Its amount in the chalcophyllite is estimated by geochemists to 0.2 per cent. Taking this conducting structure as a test area pilot deep magnetotelluric (MT) soundings have been carried out and we determined - the structure of the conductivity anomaly due to 0.2 per cent meta anthracite in the K-R window and its surroundings - the different kinds of MT distortions as lateral (side) effect of the conductor appearing in the crust and mantle - the most probable depth of the conductive asthenosphere at the border of the Pannonian Basin (having extreme shallow asthenosphere). The obtained ~140 km depth is in correlation with value of the asthenospheric map based mainly on seismic data

Linear systems with adiabatic fluctuations

We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of fluctuations and 1/|\mu| refers to the time scale of evolution of the unperturbed system to obtain a linear differential equation for the average solution. The theory is applied to the problems of a damped harmonic oscillator and diffusion in a turbulent fluid. The result is the realization of `renormalized' diffusion constant or damping constant for the respective problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page

Lagrangian Variational Framework for Boundary Value Problems

A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is implemented through a Lagrangian framework that allows to account for (i) a variety of forces including dissipative acting at the boundary; (ii) a multitude of features of interactions between the boundary and the interior fields when the boundary fields may differ from the boundary limit of the interior fields; (iii) detailed pictures of the energy distribution and its flow; (iv) linear and nonlinear effects. We provide a number of elucidating examples of the structured boundary and its interactions with the system interior. We also show that the proposed approach covers the well known boundary value problems.Comment: 41 pages, 3 figure

Theory of Adiabatic fluctuations : third-order noise

We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$, where $\alpha$ is the strength of fluctuations and $|\mu|$ is the damping rate. We show that probability distribution functions obey the differential equations of motion which contain third order terms (beyond the usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of adiabatic fluctuations in velocity space which is the counterpart of Brownian motion for fast fluctuations, has been solved exactly. The characteristic function and the associated probability distribution function are shown to be of stable form. The linear dissipation leads to a steady state which is stable and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.

Minimal Work Principle and its Limits for Classical Systems

The minimal work principle asserts that work done on a thermally isolated equilibrium system, is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well-defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For non-ergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte

A summary of WIND magnetic clouds for years 1995-2003: model-fitted parameters, associated errors and classifications

International audienceInterplanetary magnetic clouds (MCs) have been identified for the first 8.6 years of the WIND mission, and their magnetic field structures have been parameter-fitted by a static, force free, cylindrically-symmetric model (Lepping et al., 1990) with various levels of success. This paper summarizes various aspects of the results of the model fitting by providing: seven estimated model fit-parameter values for each of the 82 MCs found, their objectively determined quality estimates, closest approach vectors (in two coordinate frames), fit-parameter errors for the cases of acceptable quality (50 cases, or 61%), axial magnetic fluxes, axial current densities, and total axial current - as well as some examples of MC profiles for various conditions and "categories" for each case (e.g. Bz: N?S or S?N, etc.). MC quality is estimated from a quantitative consideration of a large set of parameters, such as the chi-squared of the model fit, degree of asymmetry of the B profile, and a comparison of two means of estimating radius. This set of MCs was initially identified by visual inspection of relevant field and plasma data. Each resulting MC candidate is then tested through the use of the MC parameter model, for various adjusted durations to determine the best fit, which helps to refine the boundary-times. The resulting MC set is called Set 1. Another, larger, set (Set 2) of MCs is identified through an automated program whose criteria are based on general MC plasma and field characteristics at 1AU determined through past experience. Set 1 is almost fully contained within Set 2, whose frequency of occurrence better matches that of the sunspot cycle than Set 1. The difference-set (Set 2-Set 1) is referred to as the magnetic cloud-like (MCL) set, whose members do not very well represent good flux ropes through modeling. We present a discussion of how a MC's front boundary is specifically identified in terms of multi-parameter considerations (i.e. any one or more of: increase in B, directional discontinuity, magnetic hole in B, drop in proton plasma beta, B-fluctuation level change, proton temperature drop, etc.), as well as through the application of the flux rope model. Also presented are examples of unusual MCs, as well as some commonly occurring relationships, such as the existence and frequency (approx. 1/2 the time) of upstream interplanetary shocks, and less frequent internal shocks

Does the Boltzmann principle need a dynamical correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)] which differs from the one that follows from the Boltzmann principle S = k log (Omega(E)) via the thermodynamic relation 1/T= dS/dE by additional terms of "dynamical" character, which are argued to correct and generalize the Boltzmann principle for small systems (here Omega(E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker-Planck formalism of Bianucci et al. is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the "volume" entropy S = k log (Phi(E)) via the thermodynamic relation above for systems of any number of degrees of freedom (Phi(E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al. and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.Comment: REVTeX 4, 10 pages, 2 figures. Accepted to J. Stat. Phy

Major Geomagnetic Storms (Dst less than or equal to -100 nT) Generated by Corotating Interaction Regions

Seventy-nine major geomagnetic storms (minimum Dst less than or equal to -100 nT) observed in 1996 to 2004 were the focus of a Living with a Star Coordinated Data-Analysis Workshop (CDAW) in March, 2005. In 9 cases, the storm driver appears to have been purely a corotating interaction region (CIR) without any contribution from coronal mass ejection-related material (interplanetary coronal mass ejections, ICMEs). These storms were generated by structures within CIRs located both before and/or after the stream interface that included persistently southward magnetic fields for intervals of several hours. We compare their geomagnetic effects with those of 159 CIRs observed during 1996 - 2005. The major storms form the extreme tail of a continuous distribution of CIR geoeffectiveness which peaks at Dst approx. -40 nT but is subject to a prominent seasonal variation of - 40 nT which is ordered by the spring and fall equinoxes and the solar wind magnetic field direction towards or away from the Sun. The O'Brien and McPherron [2000] equations, which estimate Dst by integrating the incident solar wind electric field and incorporating a ring current loss term, largely account for the variation in storm size. They tend to underestimate the size of the larger CIR-associated storms by Dst approx. 20 nT. This suggests that injection into the ring current may be more efficient than expected in such storms. Four of the nine major storms in 1996 - 2004 occurred during a period of less than three solar rotations in September - November, 2002, also the time of maximum mean IMF and solar magnetic field intensity during the current solar cycle. The maximum CIR-storm strength found in our sample of events, plus additional 23 probable CIR-associated Dst less than or equal to -100 nT storms in 1972 - 1995, is (Dst = -161 nT). This is consistent with the maximum storm strength (Dst approx. -180 nT) expected from the O'Brien and McPherron equations for the typical range of solar wind electric fields associated with CIRs. This suggests that CIRs alone are unlikely to generate geomagnetic storms that exceed these levels