Characterisation of unbounded resources of a social system within the sociological interpretation has resulted in a large number of different notions, which are relevant in different situations. From the view point of statistical mechanics, these notions resemble free energy. In this paper the concept of social free energy is introduced and first steps toward its development presented. The soci...

One of the most appealing heuristic devices for unders tanding when a phase transition will take place is to consider the balance of energy versus entropy. Probably the simplest example is the well-known (9'27) heuristic a rgument for the absence of phase transitions in one-dimensional systems with short-range forces: Suppose that there were two distinct phases with the same bulk free energy. T...

Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for β < βc, where βc denotes the nearest singularity of the free energy on the real axis. The accessible temperature range is thus the conf...

The quark contribution to the free energy of a hot quark-gluon plasma is calculated to leading order in hard-thermal-loop (HTL) perturbation theory. This method selectively resums higher order corrections associated with plasma effects, such as screening, quasiparticles, and Landau damping. Comparing to the weak-coupling expansion of QCD, the error in the one-loop HTL free energy is of order αs...

Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of findi...

The scaling properties of the soft-sphere potential allow the derivation of an exact expression for the pressure of a frozen liquid, i.e., the pressure corresponding to configurations which are local minima in its multidimensional potential energy landscape. The existence of such a relation offers the unique possibility for testing the recently proposed extension of the liquid free energy to gl...

We address some problems arising in the mathematical modeling of nematic elastomers with variable step length tensors and directors with non-uniform length (which represents, in turn, the nonuniform prolate spheroid shapes). Using a similar idea of the Ericksen theory for liquid crystals with variable degree of orientation, we introduce a non-unit vector, called the shape parameter, to describe...

We consider the accuracy of several methods for combining forward and reverse free-energy perturbation averages for two systems ~labeled 0 and 1!. The practice of direct averaging of these measurements is argued as not reliable. Instead, methods are considered of the form b(A12A0) 52ln@^w(u)exp(2bu/2)&0 /^w(u)exp(1bu/2)&1# , where A is the free energy, b51/kT is the reciprocal temperature, u5U1...

The large discrepancy between the values of the free energy for DNA dinucleotides (or dimers) measured by different teams has raised a yet unsettled debate. Here the free energy is fitted by a three parameter empiric formula derived in the framework of the crystal basis model of genetic code. Sum rules are derived and compared satisfactorily with the data. On the basis of theoretical and phenom...

A defect coupling to the square of the order parameter in a nearly quantum-critical magnet can nucleate an ordered droplet while the bulk system is in the paramagnetic phase. We study the influence of long-range spatial interactions of the form r on the droplet formation. To this end, we solve a Landau-Ginzburg-Wilson free energy in saddle point approximation. The longrange interaction causes t...