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A small object hidden in a multiple scattering medium is accurately located using a continuous light source. Good agreement between theory and experiment is found.

This paper summarizes the recent state of the art of the following topics presented at the FQMT'04 conference: Quantum, mesoscopic and (partly) classical thermodynamics; Quantum limits to the second law of thermodynamics; Quantum measurement; Quantum decoherence and dephasing; Mesoscopic and nano-electro-mechanical systems; Classical molecular motors, ratchet systems and rectified motion; Quantum Brownian motion and Quantum motors; Physics of quantum computing; and Relevant experiments from the nanoscale to the macroscale. To all these subjects an introduction is given and the recent literature is broadly overviewed. The paper contains some 450 references in total., 31 pages, 455 references with titles

A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''. 2) In work extraction from two-temperature setups, the presence of correlations can push the effective efficiency beyond the Carnot bound. 3) In the presence of level crossing, non-slow changes may be more optimal than slow ones., Comment: 5 pages. Talk given at Physics of Quantum Electronics (PQE2004), Snowbird, by Th.M. Nieuwenhuizen

Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics (``ergotropy'') is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of work extraction that contrast the thermodynamic intuition are discussed, e.g. a state with larger entropy than another may produce more work, while correlations may increase or reduce the ergotropy.

Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behavior. Exactly solvable examples are the Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath, e.g. an ion in a Penning trap, and a spin immersed in a bosonic bath, as occurs in NMR physics. It appears that the Clausius inequality $\dbarrm Q\le T\d S$ can be violated. For non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Experimental setups for testing some of the effects are discussed., Comment: Invited talk at `Physics of Quantum Electronics 33', Snowbird, January 2003. 13 pages, 2 figures

The spin-boson model, often used in NMR and ESR physics, quantum optics and spintronics, is considered in a solvable limit to model a spin one-half particle interacting with a bosonic thermal bath. By applying external pulses to a non-equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale $\T_2$ inherent to transversal (`quantum') fluctuations. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a violation of the Clausius inequality and the Thomson formulation of the second law (cycles cost work) for the two-level system. Starting from a fully disordered state, coherence can be induced by employing the bath. Due to this, a gain from a positive-temperature (inversion-free) two-level system is shown to be possible., 4 pages revtex

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equations for the order parameters and effective correlation and response function typical for neural networks. The stationary limit corresponds to the thermodynamic results. Numerical calculations illustrate our findings., 9 pages Latex including 3 eps figures, Addition of an author in the HTML-abstract unintentionally forgotten, no changes to the manuscript

A model glass with fast and slow processes is studied. The statics is simple and the facilitated slow dynamics is exactly solvable. The main features of a fragile glass take place: Kauzmann transition, Vogel-Fulcher law, Adam-Gibbs relation and aging. The time evolution can be so slow that a quasi-equilibrium occur at a time dependent effective temperature. The same effective temperature is derived from the Fluctuation-Dissipation ratio, which supports the applicability of out of equilibrium thermodynamics., Contribution to the Proceedings of the ESF SPHINX meeting `Glassy behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001). To appear in a special issue of J. Phys. Cond. Matt

In a $p$-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change in the course of time. The spins are coupled to a heat bath with temperature $T$, while the coupling constants are coupled to a bath having temperature $T_{J}$. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, $n=T/T_J$. For $p>2$ there occur at low temperatures two different glassy phases, depending on the value of $n$. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is the essentially non-equilibrium effect. The predictions of longtime dynamics and infinite-time statics differ only for $n2$. For $p=2$ correlation of the disorder (leading to a non-zero $n$) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the broken-ergodicity dynamics in the usual spin-glass models and non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived., revtex, 28 pages, 7 figures, 3 tables

A class of statistical systems is considered where different degrees of freedom have well-separated characteristic times, and are described by different temperatures. The stationary state is a nonequilibrium state with a heat flow. A generalized statistical thermodynamics is constructed and a universal variational principle is proposed. Entropy production and energy dissipation occur at a constant rate. To leading order in the small ratio of the characteristic times, there exists a universal relation between them. Onsager relations in the context of heat transfer are also considered. They are always broken, except close to equilibrium.

The diffuse intensity propagating in turbid media is sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects can be described by a stationary diffusion equation, the effect of any single object being parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object (capacitance $Q$ or effective radius $R_{\rm eff}$, polarizability $P$) can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is radiative transfer theory. This formalism is worked out in detail for spheres and cylinders of the following kinds: totally absorbing (black), transparent, and totally reflecting., 31 pages, 2 tables, 7 figures. To appear in Eur. J. Phys. B

A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ``mesoscopic'' level and is derived from the ``microscopic'' wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. In the second part the approach is extended to mesoscopic correlations between multiple scattered intensities which arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to micro waves, sound waves and non-interacting electrons., Comment: Review. 86 pages Latex, 32 eps-figures included. To appear in Rev. Mod. Phys

In order to find out whether there exists a thermodynamic description of the glass phase, the Ehrenfest relations along the glass transition line are reconsidered. It is explained that the one involving the compressibility is always satisfied, and that the one involving the specific heat is principally incorrect. Thermodynamical relations are presented for non-ergodic systems with a one-level tree in phase space. They are derived for a spin glass model, checked for other models, and expected to apply, e.g., to glass forming liquids. The second Ehrenfest relation gets a contribution from the configurational entropy., Comment: 4 pages revtex, to appear in Phys. Rev. Lett

Multiple scattering of polarised electromagnetic waves in diffusive media is investigated by means of radiative transfer theory. The method becomes exact in several situations of interest, such as a thick-slab experiment (slab thickness L >> mean free path $\ell >> wavelength ��)$. The present study is restricted to Rayleigh scattering. It incorporates in a natural way the dependence on the incident and detected polarisations, and takes full account of the internal reflections at the boundaries of the sample, due to the possible mismatch between the mean optical index n of the medium and that n_1 of the surroundings. Quantities of interest, such as the polarisation-dependent angle-resolved mean diffuse intensity in reflection and in transmission and the shape of the cone of enhanced backscattering, are predicted in terms of solutions to Schwarzschild-Milne equations. The latter are obtained analytically both in the absence of internal reflections and in the regime of a large index mismatch., To appear in Journal de Physique I (March 1997). Figures available upon email request to luck@spht.saclay.cea.fr

On the basis of a recent field theory for site-disordered spin glasses a Ginzburg-Landau free energy is proposed to describe the low temperatures glassy phase(s) of site-disordered magnets. The prefactors of the cubic and dominant quartic terms change gradually along the transition line in the concentration-temperature phase diagram. Either of them may vanish at certain points $(c_*, T_*)$, where new transition lines originate. The new phases are classified, 6 pages Revtex, 5 figures. To appear in J. Phys. A. Lett

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive., 9 pages, Revtex, with eps figures,to appear in Phys Rev B

A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry breaking. The order parameter function is solved exactly in the whole low temperature phase. The zero field cooled susceptibility remains finite at low $T$. Next a quantum version of the system is considered. Whereas the magnetic properties are not altered qualitatively, the thermodynamics is now regular at small temperatures., 4 pages postscript. Revised version, to appear in Phys. Rev. Lett

The probability distribution of the total transmission is studied for waves multiple scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulant of this distribution is presented. Within a diagrammatic approach a theory is developed which relates the third cumulant normalized to the average, $\langle \langle T_a^3 \rangle \rangle$, to the normalized second cumulant $\langle \langle T_a^2 \rangle \rangle$. For a broad Gaussian beam profile it is found that $\langle \langle T_a^3 \rangle \rangle= \frac{16}{5} \langle \langle T_a^2 \rangle \rangle^2 $. This is in good agreement with data of optical experiments., 16 pages revtex, 8 separate postscript figures

The spherical model for spins describes ferromagnetic phase transitions well, but it fails at low temperatures. A quantum version of the spherical model is proposed. It does not induce qualitative changes near the phase transition. However, it produces a physical low temperature behavior. The entropy is non-negative. Model parameters can be adapted to the description of real quantum spins. Several applications are discussed. Zero-temperature quantum phase transitions are analyzed for a ferromagnet and a spin glass in a transversal field. Their crossover exponents are presented., 4 pages postscript. Revised version, to appear in Phys. Rev. Lett

Propagation of light in media with a small density of resonant atoms at quenched random positions is studied. It is found that the transport speed is reduced substantially due to dwell effects when the atoms are close to resonance. Besides propagation of real photons, the transport channel of nonradiative transfer due to the resonance dipole-dipole interaction between excited and ground state atoms is considered. The transport equation including both transport channels is derived. The diffusion coefficient and the dielectric constant are found. The weight of the nonradiative channel increases with the density of resonant atoms, n, and becomes essential when nλ3 approaches unity, where λ is the wavelength of the light.

We report the first measurement of the distrubution function of the fluctuations on the total transmission of multiple scattered light. The shape of the distribution is predominantly Gaussian. A non-Gaussian contribution to the distribution function is found, caused by correlation in the cubed intensity. The scattering diagrams responsible for this new correlation are calculated without free parameters, and a good agreement is found between experiment and theory.

Recent observations put forward that quasars are black holes with a magnetic dipole moment and no event horizon. To model hairy black holes a quantum field for hydrogen is considered in curved space, coupled to the scalar curvature. An exact, regular solution for the interior metric occurs for supermassive black holes. The equation of state is p = −ρc2/3.

In realistic spin glasses a fraction c of spins is located at random positions. Their couplings are determined by the relative spin positions. For such systems a field theory is formulated. In a certain mean-field limit it generalizes the Sherrington-Kirkpatrick free energy of a random bond spin glass. In general, an infinity of multistate overlaps occurs, as in the diluted random bond spin glass of Viana and Bray. For small c there occurs a percolation transition for short-range exchange and the "concentration scaling" TG ~ c for RKKY couplings.

Semi-ballistic transport occurs when cavities have a moderate amount of elastic scattering, so that transport in the long direction(s) become diffusive. Transmission patterns are studied in this regime for disordered waveguides and for Fabry-Perot interferometers with "dirty" mirrors. The results have implications for mesoscopic conductors at zero temperature. It is shown that the average "Ohmic" conductivity of disordered quantum wires in the semi-ballistic regime decreases significantly when a new transmission channel is opened; for films this occurs in a universal way. The transmission current of certain GaAs-AlGaAs double-barrier quantum wells is shown to have a broad resonance linewidth, induced by intrinsic irregularities in the barrier interfaces.

The speckle correlation function of light transmitted through a disordered slab is studied. A multiple scattering expansion for resonant point scatterers is employed. Taking into account the influence of boundary layers and absorption, the general expression for the correlation function is presented. It is shown that the Langevin treatment and the diagrammatic approach coincide.

The influence of one extra static scatterer on multiple scattered classical waves is considered. It is shown how to connect two “diffusions” or “ladders”. Secondly, the interaction vertex of four diffusions (“Hikami box”) is generalized to non-static situations and the presence of absorption. Beyond the second order Born approximation, eight diagrams are relevant.

The transport of radiation in the bulk of multiply scattering media is well understood within the diffusion approximation. Such a description does not hold in the skin layers, where the transport mechanism crosses over from free propagation to diffusive propagation, or vice versa. In this work, we examine the effects of the skin layers of optically thick slabs on various quantities, including the angularly resolved diffuse reflection and transmission and the shape of the enhanced backscattering cone. This study is based on the ladder approximation to the multiple-scattering expansion. It does not rely on the diffusion approximation and incorporates a systematic treatment of the internal reflections which take place when the random-scattering medium and the outside have two different optical indices, in an arbitrary ratio m. Many exact results are recovered in the absence of internal reflections (m=1). A systematic approach describes accurately the large-index-mismatch regime (m\ensuremath{\rightarrow}0 or \ensuremath{\infty}), where the improved diffusion approximation is shown to become exact asymptotically. The analytic predictions of the large-index-mismatch approach are compared in a detailed way with numerical results and with the outcomes of previous works.

In a demixed binary-fluid system, a wetting layer of the most dense phase can intrude between the lighter phase and the vapour. Due to the first-order character of the wetting transition, a hysteresis can be observed leading to the formation of either a very thin or a thick film at the liquid/vapour interface. Ellipsometry experiments are presented which indicate that the thin film grows in layers with a thickness of the order of the molecular diameter, rather than continuously. The data show that a series of first-order layering transitions takes place at the interface.

The thermally induced denaturation of DNA in the presence of attractive solid surface is studied. The two strands of DNA are modeled via two coupled flexible chains without volume interactions. If the two strands are adsorbed on the surface, the denaturation phase-transition disappears. Instead, there is a smooth crossover to a weakly naturated state. Our second conclusion is that even when the inter-strand attraction alone is too weak for creating a naturated state at the given temperature, and also the surface-strand attraction alone is too weak for creating an adsorbed state, the combined effect of the two attractions can lead to a naturated and adsorbed state., 21 pages, 1 figure

The mapping L i =1+x i L i−1 is studied. The xi, i=1, 2, 3, are independent random variables with common distribution. This mapping describes growth under fluctuating conditions, as may occur, e.g., in biology and economics. It also shows up in the grand canonical description of a directed polymer, bound to a wall of a random (1+1)-dimensional medium, in the limit where the polymer length goes to infinity. It is proven here that there is no self-averaging in this “thermodynamic” limit. Distribution functions which show this behavior explicitly are derived.

Models of a directed polymer chain are studied in the presence of disorder in two and three dimensions, which describe adsorption-desorption transitions due to an attracting substrate. In particular, the free energy and the scaling behavior of the monomer concentration profile in the vicinity of the transition are calculated using a grand canonical ensemble. The scaling form differs from that found in the case of no disorder.

The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state of lower entropy. The extensive entropy loss, called complexity or information entropy, is calculated by analysis of the metastable (TAP) states. This yields a well behaved thermodynamics of the dynamical transition. The multitude of glassy states also implies an extensive difference between the internal energy fluctuations and the specific heat. In the directed polymer problem there occurs a thermodynamic phase transition in non-extensive terms of the free energy. At low temperature the polymer condenses in a set of highly degenerate metastable states.

This paper starts with a review of work on singularities in the spectral density of random harmonic chains. Detailed descriptions of singular behavior near the maximal frequency, near special frequencies and near island frequencies are discussed. Next the site-disordered Anderson model is considered. Here the discussion is limited to the singularity in the density of states near the low-energy band edge for systems with arbitrary disorder in dimensions d = 1, 2, 3. In a specific example it is shown that renormalization improves the prediction for the band tail quantitatively.

This paper deals with independent particles diffusing on a line with traps at random positions. It is shown how the long-time decay of the survival probability is exhanced when particles do not necessarily disappear upon hitting a trap. The results are compared with predictions for a model where particles are either absorbed or reflected by traps.

A model is presented which describes magnetic properties of high-Tc superconductors when flux creep is the leading mechanism for dissipation. This model reduces the behaviour of a complex current pattern to the behaviour of essentially one single current loop which contains a fluctuating number of flux quanta. It is shown that the dynamics of such a system describes widely observed phenomena such as logarithmic decay of the magnetization, broadening of the resistive transition as a function of an external field and nonlinearity in the a.c.-susceptibility. Away from equilibrium, fluctuations in the magnetization and even harmonics in the a.c.-susceptibility decay algebraically in time.

An argument is given why the classical theory called Stochastic Electrodynamics may reproduce scattering and ionization experiments of electrons on atomic hydrogen.

The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement, regarded as a process of quantum statistical mechanics. Schr\"odinger cat terms involving both the system and the apparatus, die out very quickly, while the registration is a process taking the apparatus from its initially metastable state to one of its stable final states. The occurrence of Born probabilities can be inferred at the macroscopic level, by looking at the pointer alone. Apparent non-unitary behavior of the measurement process is explained by the arisal of small many particle correlations, that characterize relaxation., Comment: 13 pages, discussion of pre-measurement added. World Scientific style. To appear in proceedings "Beyond The Quantum", Th.M. Nieuwenhuizen et al, eds, (World Scientific, 2007)

In the Relativistic Theory of Gravitation, space‐time is Minkowskian, and gravitation is a physical field, next to electromagnetism. The bimetric coupling of Riemann and Minkowski metrics allows to defines a unique, local gravitational energy density. The case of a positive cosmological constant is considered. For cosmology, the ΛCDM model is covered, while there appears a form of inflation at early times. Furthermore, both the total energy and the zero point energy vanish.Within this theory an exact solution is presented for the interior of supermassive black holes (M⋆∼108M⊙. They are consistent with a Bose‐Einstein condensates of densely packed H‐atoms. The solution is regular everywhere with a specific shape at the origin. The redshift at the horizon is finite but large, z∼1014M⋆/M. The problem is exactly and self‐consistently solved within a quantum field theoretic approach for the matter. Its direct back‐reaction on the metric is 100%. In the BEC ground state, the binding energy equals 71% of the res...

The minimal work principle asserts that work done on a thermally isolated equilibrium system, is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well-defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For non-ergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed., Comment: 4 + epsilon pages, 1 figure, revtex

We show that for two classical brownian particles there exists an analog of continuous-variable quantum entanglement: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot be prepared via mixing of any factorized distributions referring to the two particles in separate. This is possible for particles which interacted in the past, but do not interact in the present. Three factors are crucial for the effect: 1) separation of time-scales of coordinate and momentum which motivates the definition of coarse-grained velocities; 2) the resulting uncertainty relations between the coordinate of the brownian particle and the change of its coarse-grained velocity; 3) the fact that the coarse-grained velocity, though pertaining to a single brownian particle, is defined on a common context of two particles. The brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the brownian motion. We discuss possibilities of its experimental realizations in examples of macroscopic brownian motion., Comment: 18 pages, no figures

In a recent paper Hawking has argued that there is no information loss in black holes in asymptotically AdS spacetimes. We remind that there are several types of information (entropy) in statistical physics -- fine grained (microscopic) and coarse grained (macroscopic) ones which behave differently under unitary evolution. We suggest that the coarse grained information of the rest of the Universe is lost while fine grained information is preserved. A possibility to develop in quantum gravity an analogue of the Bogoliubov derivation of the irreversible Boltzmann and Navier - Stokes equations from the reversible mechanical equations is discussed., Comment: 8 pages

A suitable sequence of sharp pulses applied to a spin coupled to a bosonic bath can cool its state, i.e., increase its polarization or ground state occupation probability. Starting from an unpolarized state of the spin in equilibrium with the bath, one can reach very low temperatures or sizeable polarizations within a time shorter than the decoherence time. Both the bath and external fields are necessary for the effect which comes from the backreaction of the spin on the bath. This method can be applied to cool at once a disordered ensemble of spins. Since the bath is crucial for this mechanism, the cooling limits are set by the strength of its interaction with the spin(s)., Comment: 4 pages. Accepted in PRL

The minimal work principle states that work done on a thermally isolated equilibrium system is minimal for adiabatically slow (reversible) realization of a given process. This principle, one of the formulations of the second law, is studied here for finite (possibly large) quantum systems interacting with macroscopic sources of work. It is shown to be valid as long as the adiabatic energy levels do not cross. If level crossing does occur, counter examples are discussed, showing that the minimal work principle can be violated and that optimal processes are neither adiabatically slow nor reversible. The results are corroborated by an exactly solvable model., Comment: 13 pages, revtex, 2 eps figures

A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without momenta in the Hamiltonian can be described, which may lead to different symmetry classes. Two models that show this difference are analyzed. Both models are exactly solvable and their phase diagram is analyzed. A transversal external field leads to a phase transition line that ends in a quantum critical point. The two considered symmetries of the Hamiltonian considered give different critical phenomena in the quantum critical region. The model with momenta is argued to be analog to the large-N limit of an SU(N) Heisenberg ferromagnet, and the model without momenta shares the critical phenomena of an SU(N) Heisenberg antiferromagnet., 22 pages

The Clausius inequality, one of the classical formulations of the second law, was recently found to be violated in the quantum regime. Here this result is formulated in the context of a mesoscopic or nanoscale linear RLC circuit interacting with a thermal bath. Previous experiments in this and related fields are analyzed and possibilities of experimental detection of the violation are pointed out. It is discussed that recent experiments reached the range of temperatures, where the effect should be visible, and that a part of the proposal was already confirmed., Comment: 5 pages revtex 4. No figures

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., 13 pages, revtex, 2 eps figures

We investigate a mean-field approach to a quantum brownian particle interacting with a quantum thermal bath at temperature $T$, and subjected to a non-linear potential. An exact, partially classical description of quantum brownian motion is proposed, which uses negative probabilities in its intermediate steps. It is shown that properties of the quantum particle can be mapped to those of two classical brownian particles in a common potential, where one of them interacts with the quantum bath, whereas another one interacts with a classical bath at zero temperature. Due to damping the system allows a unique and non-singular classical limit at $\hbar \to 0$. For high $T$ the stationary state becomes explicitly classical. The low-temperature case is studied through an effective Fokker-Planck equation. Non-trivial purely quantum correlation effects between the two particles are found., Comment: 13 pages, 0 figures, revtex

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 revtex