Energy representation for nonequilibrium brownian-like systems: steady states and fluctuation relations.

Stochastic dynamics in the energy representation is used as a method to represent nonequilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin equation with multiplicative noise. Properties of the steady states are examined by solving the Fokker-Planck equation for the energy distribution functions. The generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator. From this theorem, a number of entropy and fluctuation relations such as the Evans-Searles fluctuation theorem, the Hatano-Sasa identity, and the Jarzynski's equality are derived.

Interaction of foreign macroparticles in a cholesteric liquid crystal.

We calculate the interaction energy between spherical macroparticles immersed in a cholesteric liquid crystal due to the elastic deformation of the director field. We assume weak anchoring on the surface of the macroparticles and obtain the expression of the interaction energy that is valid for particle radius and interparticle distance sufficiently smaller than the cholesteric pitch. The resultant form of the interaction energy is more complex than that in a nematic liquid crystal. One of the characteristics is its dependence on the particle position as well as the interparticle distance, which arises from the intrinsic structure of a cholesteric liquid crystal, i.e., the absence of translational symmetry due to helical periodicity and local nematic ordering whose orientation depends on the position.

Interaction of particles in a deformed nematic liquid crystal.

We investigate how the interaction of particles mediated by an elastic deformation of a nematic liquid crystal is influenced by the initial deformation of the director field. To this end, we calculate the interaction energy between particles in a nematic cell with hybrid boundary conditions, homeotropic on the surface of one confining plate and planar on the other. We find an analytic form of the interaction energy in the case of weak anchoring on the surface of the particle. This interaction energy sensitively depends on the position of the two particles as well as the interparticle distance and can be nonmonotonic with a minimum in its landscape. This nontrivial energy landscape might lead to a chainlike superstructure of particles.