Arrows of Time and the Anisotropic Properties of CMB

The relation between the thermodynamical and cosmological arrows of time is usually viewed in the context of the initial conditions of the Universe. It is a necessary but not sufficient condition for ensuring the thermodynamical arrow. We point out that in the Friedmann-Robertson-Walker Universe with negative curvature, k=-1, there is the second necessary ingredient. It is based on the geodesic mixing - the dynamical instability of motion along null geodesics in hyperbolic space. Kolmogorov (algorithmic) complexity as a universal and experimentally measurable concept can be very useful in description of this chaotic behavior using the data on Cosmic Microwave Background radiation. The formulated {\it curvature anthropic principle} states the negative curvature as a necessary condition for the time asymmetric Universe with an observer.Comment: Revtex, to appear in the proceedings of the workshop THE CHAOTIC UNIVERSE, Eds.V.G.Gurzadyan, R.Ruffini, World Sc

Free energy for non-equilibrium quasi-stationary states

We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy. Three conditions are needed for the existence of free energy in this non-equilibrium system: time-scale separation between variables of the system, partial controllability (external fields couple only with the slow variable), and an effective detailed balance. These conditions are facilitated in the continuous limit for the slow variable. In contrast to its equilibrium counterpart, the non-equilibrium free energy can increase with temperature. One example of this is that entropy reduction by means of external fields (cooling) can be easier (in the sense of the work cost) if it starts from a higher temperature.Comment: 8 pages, 2 figure