Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universalit...

We discover a Ising-type duality in the general N -state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N = 2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small k) to those of another chiral Potts model at a high temperature (of k). The τ -model and chiral Potts model on the dual lattice are establish...

In 1949, a Nobelist Last Onsager considered liquid flows with velocities changing as r for spatial points at distance r, and conjectured that the threshold value α = 1/3 separates the two possible regimes: for α > 1/3 energy is always preserved, while for α < 1/3 energy is possibly not preserved. In this paper, we provide a simple pedagogical explanation for this conjecture. 1 Formulation of th...

We consider extensions of excluded volume interactions for complex corpora that generalize simple rod-like particles. The Onsager equation can be defined for quite general configuration spaces, and the dimension reduction of the phase space in the limit of highly intense interaction can be shown. The formalism describes both freely articulated and interacting N-rods and the example of interacti...

We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our basic physical assumptions comprise (a) a chaoticity hypothesis for the nonconserved currents carried by these observables, (b) an extension of Onsager’s regre...

The effects of mobility corrections on carrier ampholytes are studied at various ampholyte concentrations to understand protein behavior during IEF. IEF simulations are conducted in the presence of 25 biprotic carrier ampholytes within a pH range of 6-9 after applying the Onsager-Debye-Hückel correction to the carrier ampholytes. Two model proteins with ten charge states but without ionic stren...

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability density function (Onsager). As in density-functional theories, the suggested free energy is a functional of spatially-dependent orientation distributi...

In a four terminal sample, microscopic time reversibility leads to symmetry relations between resistance measurements where the role of current and voltage leads are exchanged. These reciprocity relations are a manifestation of general Onsager-Casimir symmetries in equilibrium systems. We investigate experimentally the validity of time-reversal symmetry in a GaAs/Ga_{1-x}Al_{x}As Hall bar irrad...

We investigate theoretically the violations of Einstein and Onsager relations and the thermodynamic efficiency for a single processive motor operating far from equilibrium using an extension of the two-state model introduced by Kafri et al. [Biophys. J. 86, 3373 (2004)10.1529/biophysj.103.036152]. With the aid of the Fluctuation Theorem, we analyze the general features of these violations and t...

We study suspensions of semiflexible colloidal rods and biopolymers using an Onsager-type second-virial functional for a segmented-chain model. For mixtures of thin and thick fd virus particles, we calculate full phase diagrams, finding quantitative agreement with experimental observations. We show that flexibility, which renders the rods effectively shorter and thicker depending on the state p...