A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson formulation (`cyclic changes cost energy'), applied to equilibrium. This formulation of the second law is a property akin to particle conservation (normalization of the wavefunction). It has been stricktly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble. As the derivation does not assume time-inversion-invariance, it is applicable to situations where persistent current occur. This clear-cut derivation allows to revive the ``no perpetuum mobile in equilibrium'' formulation of the second law and to criticize some assumptions which are widespread in literature. The result puts recent results devoted to foundations and limitations of the second law in proper perspective, and structurizes this relatively new field of research.Comment: Revised version. Redundant assumption omitted. Microcanonical ensemble included. Reference added. 7 pages revte

Breakdown of the Landauer bound for information erasure in the quantum regime

A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing \d S of its entropy must release at least an amount |\dbarrm Q|=T|\d S| of heat. This serves as a basis for the Landauer principle, which puts a lower bound $T\ln 2$ for the heat generated by erasure of one bit of information. Here we show that in the world of quantum entanglement this law is broken. A quantum Brownian particle interacting with its thermal bath can either generate less heat or even {\it adsorb} heat during an analogous squeezing process, due to entanglement with the bath. The effect exists even for weak but fixed coupling with the bath, provided that temperature is low enough. This invalidates the Landauer bound in the quantum regime, and suggests that quantum carriers of information can be much more efficient than assumed so far.Comment: 13 pages, revtex, 2 eps figure

Green function Retrieval and Time-reversal in a Disordered World

We apply the theory of multiple wave scattering to two contemporary, related topics: imaging with diffuse correlations and stability of time-reversal of diffuse waves, using equipartition, coherent backscattering and frequency speckles as fundamental concepts.Comment: 1 figur

Pascal Principle for Diffusion-Controlled Trapping Reactions

"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A" particle, which performs a lattice random walk in presence of a concentration of randomly moving traps "B", and gets annihilated upon encounters with any of them. We prove here that at sufficiently large times for both perfect and imperfect trapping reactions, for arbitrary spatial dimension "d" and for a rather general class of random walks, the "A" particle survival probability is less than or equal to the survival probability of an immobile target in the presence of randomly moving traps.Comment: 4 pages, RevTex, appearing in PR

Chaotic, memory and cooling rate effects in spin glasses: Is the Edwards-Anderson model a good spin glass?

We investigate chaotic, memory and cooling rate effects in the three dimensional Edwards-Anderson model by doing thermoremanent (TRM) and AC susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of re-initialization processes in temperature change experiments (TRM or AC). A detailed comparison with AC relaxation experiments in the presence of DC magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.Comment: 17 pages, 10 figures. The original version of the paper has been split in two parts. The second part is now available as cond-mat/010224

Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation

The experimental time scale dependence of thermodynamic relations in out-of-equilibrium systems with aging phenomena is investigated theoretically by using only aging properties of the two-time correlation functions and the generalized fluctuation-dissipation theorem (FDT). We show that there are two experimental time regimes characterized by different thermal properties. In the first regime where the waiting time is much longer than the measurement time, the principle of minimum work holds even though a system is out of equilibrium. In the second regime where both the measurement time and the waiting time are long, the thermal properties are completely different from properties in equilibrium. For the single-correlation-scale systems such as $p$-spin spherical spin-glasses, contrary to a fundamental assumption of thermodynamics, the work done in an infinitely slow operation depends on the path of change of the external field even when the waiting time is infinite. On the other hand, for the multi-correlation-scale systems such as Sherrington-Kirkpatrick model, the work done in an infinitely slow operation is independent of the path. Our results imply that in order to describe thermodynamic properties of systems with aging it is essential to consider the experimental time scales and history of a system as a state variable is necessary.Comment: 28 pages(REVTeX), 4 figure(EPS). To be published in Phys. Rev.

Lattice theory of trapping reactions with mobile species

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an $A$ particle with any of the $B$ particles, $A$ is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables - "gates", imposed on each $B$ particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the $A$ particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time $t$, the $A$ particle survival probability is always larger in case when $A$ stays immobile, than in situations when it moves.Comment: 12 pages, appearing in PR

Non-Equilibrium Thermodynamic Description of the Coupling between Structural and Entropic Modes in Supercooled Liquids

The density response of supercooled glycerol to an impulsive stimulated thermal grating (q=0.63 micron^-1) has been studied in the temperature range (T=200-340 K) where the structure rearrangement (alpha-relaxation) and thermal diffusion occur on the same time scale. A strong interaction between the two modes occurs giving rise to a dip in the T-dependence of the apparent thermal conductivity and a flattening of the apparent alpha-relaxation time upon cooling. A non-equilibrium thermodynamic (NET) model for the long time response of relaxing fluids has been developed. The model is capable to reproduce the experimental data and to explain the observed phenomenology.Comment: to be published in PRE Rapid Commu

Thermodynamics and statistical mechanics of frozen systems in inherent states

We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular we consider three lattice models (a diluted Spin Glass, a monodisperse hard-sphere system under gravity and a hard-sphere binary mixture under gravity) undergoing a schematic ``tap dynamics'', showing via Monte Carlo calculations that the time average of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to non thermal systems.Comment: 10 pages, 16 figure