Multiscale Thermodynamics.

Multiscale thermodynamics is a theory of the relations among the levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case, but it is applicable to both static and time evolving processes in externally and internally driven macroscopic systems that are far from equilibrium and are investigated at the microscopic, mesoscopic, and macroscopic levels. In this paper we formulate multiscale thermodynamics, explain its origin, and illustrate it in mesoscopic dynamics that combines levels.

Dynamic and Renormalization-Group Extensions of the Landau Theory of Critical Phenomena.

We place the Landau theory of critical phenomena into the larger context of multiscale thermodynamics. The thermodynamic potentials, with which the Landau theory begins, arise as Lyapunov like functions in the investigation of the relations among different levels of description. By seeing the renormalization-group approach to critical phenomena as inseparability of levels in the critical point, we can adopt the renormalization-group viewpoint into the Landau theory and by doing it bring its predictions closer to results of experimental observations.

Gradient and GENERIC time evolution towards reduced dynamics.

Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables).

Dynamic Maximum Entropy Reduction.

Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways.

Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics.

Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions, however, approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is not changed by the Vlasov equation. On the other hand, density and kinetic energy density, which are integrals of the distribution function, approach spatially homogeneous states strongly, which is accompanied by growth of the hydrodynamic entropy.

Time reversal in nonequilibrium thermodynamics.

The general equation of nonequilibrium reversible-irreversible coupling (GENERIC) is studied in light of time-reversal transformation. It is shown that Onsager-Casimir reciprocal relations are implied by GENERIC in the near-equilibrium regime. A general structure which gives the reciprocal relations but which is valid also far from equilibrium is identified, and Onsager-Casimir reciprocal relations are generalized to far-from-equilibrium regime in this sense.

Mechano-chemical coupling in Belousov-Zhabotinskii reactions.

Mechano-chemical coupling has been recently recognised as an important effect in various systems as chemical reactivity can be controlled through an applied mechanical loading. Namely, Belousov-Zhabotinskii reactions in polymer gels exhibit self-sustained oscillations and have been identified to be reasonably controllable and definable to the extent that they can be harnessed to perform mechanical work at specific locations. In this paper, we use our theoretical work of nonlinear mechano-chemical coupling and investigate the possibility of providing an explanation of phenomena found in experimental research by means of this theory.