For an organisation with a Pareto-like distribution of the relevant resources we determine the social free energy and related social quantities using thermodynamical formalism. Macroscopic dynamics of the organisation is linked with the changes in the attributed thermodynamical quantities through changes in resource distribution function. It is argued that quantities of thermodynamical origin f...

We confirm Odijk’s scaling laws for (i) the average chain extension; (ii) the variance about the average extension; and (iii) the confinement free energy of a wormlike chain confined in a rectangular nanochannel smaller than its chain persistence length through pruned-enriched Rosenbluth method (PERM) simulations of asymptotically long, discrete wormlike chains. In the course of this analysis, ...

This supplement to ‘Electrowetting with Electrolytes’ gives the derivation of two general equations applicable to electrowetting with an interface between two immiscible electrolytic solutions (ITIES). The first section provides a derivation of the functional to determine the Gibbs free energy, G. This result is expressed in terms of the potential and ionic-concentration distributions for dropl...

Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for F 1 in hermitian one-matrix model. We discuss the relationship between F 1 , Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and d...

Recently I suggested that for the deconfining phase transition in a pure gauge theory, the behavior of the usual order parameter — the Polyakov loop — may be correlated with the pressure. In fact this correspondence is implicit in studies of two colors done by Engels, Fingberg, Redlich, Satz, and Weber in 1989 [1]. For two colors, the deconfining transition appears to be of second order [1–3]. ...

We show that the non-critical c = 1 string at the self-dual radius is equivalent to topological strings based on the deformation of the conifold singularity of Calabi-Yau threefolds. The Penner sum giving the genus expansion of the free energy of the c = 1 string theory at the self-dual radius therefore gives the universal behaviour of the topological partition function of a Calabi-Yau threefol...

S1. RA-SHG data for Sin-Pout and Sin-Sout geometries above and below TΩ S2. Mathematical expressions used for fitting RA-SHG patterns S3. Visualizing the 2/m1 magnetic point group symmetry of the Néel phase S4. Loop-current order in cuprates versus iridates S5. Behavior of hidden order domains under repeated thermal cycles S6. Survey of RA-SHG patterns of Sr2IrO4 across spatial regions S7. Fun...

We prove theorems characterizing the minimizers for the Cahn-Hilliard free energy functional, which is used to describe the liquid vapor phase transition (or the 2 state magnetization transition). In particular, we exactly determine the critical density for droplet formation, and the geometry of the droplets.

Jarzynski and Crooks have recently shown that equilibrium free energy differences can be computed from non-equilibrium thermodynamic path integrals. In the present paper we give a new derivation of this extraordinary relation. Our derivation which is valid for time reversible deterministic systems highlights the close relationship between the non-equilibrium free energy theorems and the fluctua...