We review recent results on the relationships between the microscopic chaos in the motion of atoms or molecules in fluids and the transport properties sustained across these macroscopic systems. In the escape-rate formalism, the transport coefficients can be expressed in terms of the positive Lyapunov exponents, the Kolmogorov-Sinai entropy per unit time or the Hausdorff dimension of a fractal ...

When a black hole is put in an empty space (zero temperature space) on which there is no matter except the matter of the Hawking radiation (Hawking field), then an outgoing energy flow from the black hole into the empty space exists. By the way, an equilibrium between two arbitrary systems can not allow the existence of an energy (heat) flow from one system to another. Consequently, in the case...

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime ...

By considering general Markov stochastic dynamics and its coarse graining, we study the framework of stochastic thermodynamics for the original and reduced descriptions corresponding to different scales. We are especially concerned with the case where the irreversible entropy production has a finite difference between the scales. We find that the sum of the increment of the nonequilibrium entro...

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, an...

Applying Gibb’s geometrical methods to the thermodynamics of H-plasmas we explore the landscape of the free energy as a function of the degrees of ionization and dissociation. Several approximations for the free energy are discussed. We show that in the region of partial ionization/dissociation the quantum Debye-Hückel approximation (QDHA) yields a rather good but still simple representation wh...

The electrical transport problems in semiconductors are nonequilibrium phenomena and most conveniently described by the hydrodynamic equations (or balance equations) that involve the directly measurable, macroscopic variables of the system [1–8]. Such nonequilibrium state-variables are the carrier density, drift velocity, and temperature in the conventional hydrodynamic description [1–4] and al...

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from ma...

New concepts in thermodynamics are further extended and combined with a principle of virtual dissipation to provide general equations of evolution of collective open chemical systems. A new definition of the chemical potential is introduced, and some new expressions for the affinity are discussed. Application of the principle of virtual dissipation leads very simply to quite general continuum f...