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A recent paper [M.H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York) 1949] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a Generalized Langevin Equation the Khinchin theorem holds.

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.

We analyze the heat transfer between two nanoparticles separated by a distance lying in the near-field domain in which energy interchange is due to the Coulomb interactions. The thermal conductance is computed by assuming that the particles have charge distributions characterized by fluctuating multipole moments in equilibrium with heat baths at two different temperatures. This quantity follows from the fluctuation-dissipation theorem for the fluctuations of the multipolar moments. We compare the behavior of the conductance as a function of the distance between the particles with the result obtained by means of molecular dynamics simulations. The formalism proposed enables us to provide a comprehensive explanation of the marked growth of the conductance when decreasing the distance between the nanoparticles.

In the first part of this article we study the hysteretic bistable response of Duffing oscillators and show ways to control the switching between stable branches of this nonlinear response. The control mechanism is either applied through a pulse that can be in phase or out of phase with the periodic driving force or through a frequency-modulated driving force. In the second part we show how memory effects in dissipation qualitatively and quantitatively alter the dynamics of Duffing oscillators. We show how memory functions corresponding to different dissipative regimes (diffusion, subdiffusion, and superdiffusion) affect the oscillator. In particular, we obtain universal power laws for the absoption when the driving frequency ω → 0. For subdiffusive memories the power law exponents ν<2, for diffusive memories ν= 2, and for superdiffusive memories ν>2.

We study the relationship between quantum screening effects and charge symmetry in the hydrogen molecule. In this model, the charge symmetry of the molecule is broken in the presence of the Thomas–Fermi potential exp(−qr )/r . We argue that screening acts as an external field that promotes charge degeneracy in the system. In the presence of screening (q = 0), the charge symmetry of the H⁺₂ molecule is broken and thus the effective nuclear charge α splits into two, α → (α, γ ), where γ is the dual charge. The effective nuclear charge α is then related to the binding energy of the electron, while the dual charge γ is responsible for the screening effect in the wavefunction. Naturally, both the energy and the wavefunction are modified by this charge degeneracy. We obtain an analytical formulation for the molecular energy with a charge degeneracy effect. To test the efficiency of our model, we analyze the behavior of the molecule’s energy as a function of the Thomas–Fermi parameter q and calculate the critical parameter q^∗ , as well as the critical dual charge γ^∗ for which the bound–unbound transition occurs. We observe an interesting super-freezing screening phenomenon for the Thomas–Fermi hydrogen molecule.

Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.