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There are several theories or processes which may underlie quantum mechanics and make it deterministic. Some references are given in the main text. Any such theory, plus a number of reasonable assumptions, implies the existence of what I have called ``special" states. The assumptions are conservation laws, obedience (up to a point) of Schrodinger's equation, and a single world, in the sense of the many worlds interpretation (the last one a consequence of any deterministic theory). This article also, for clarity, gives an example of a ``special" state. There is an experimental test of the ``special" state theory., Comment: 5 pages, 2 figures. For v2 I have added the condition (for the validity of my argument) that there not be degrees of freedom invisible to the Schrodinger equation

Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. By calculating a transport coefficient we show that indeed---at least in this case---the source of dissipation in that coefficient is the relative entropy.

An experimental test of the "special state" theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern-Gerlach setup. The "special state" theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this article background material is given on both quantum measurement and statistical mechanics aspects. For example, it is shown that future boundary conditions would not contradict experience, indicating that the fundamental equal-a-priori-probability assumption at the foundations of statistical mechanics is far too strong (since future conditioning reduces the class of allowed states). The test is based on a feature of this theory that was found necessary in order to recover standard (Born) probabilities in quantum measurements. Specifically, certain systems should have "noise" whose amplitude follows the long-tailed Cauchy distribution. This distribution is marked by the occasional occurrence of extremely large signals as well as a non-self-averaging property. The proposed test is a variant of the Stern-Gerlach experiment in which protocols are devised, some of which will require the presence of this noise, some of which will not. The likely observational schemes would involve the distinction between detection and non-detection of that "noise". The signal to be detected (or not) would be either single photons in the visible and UV range or electric fields (and related excitations) in the neighborhood of the ends of the magnets., Comment: This has already been published (see Journal reference), but I have since found an error and corrected it. See endnote 28

Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.

Possible definitions for the relative momentum of identical particles are considered.

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up., Comment: 34 pages, 4 figures, 3 tables

Several recent theories address the efficiency of a macroscopic thermodynamic motor at maximum power and question the so-called "Curzon-Ahlborn (CA) efficiency." Considering the entropy exchanges and productions in an n-sources motor, we study the maximization of its power and show that the controversies are partly due to some imprecision in the maximization variables. When power is maximized with respect to the system temperatures, these temperatures are proportional to the square root of the corresponding source temperatures, which leads to the CA formula for a bi-thermal motor. On the other hand, when power is maximized with respect to the transitions durations, the Carnot efficiency of a bi-thermal motor admits the CA efficiency as a lower bound, which is attained if the duration of the adiabatic transitions can be neglected. Additionally, we compute the energetic efficiency, or "sustainable efficiency," which can be defined for n sources, and we show that it has no other universal upper bound than 1, but that in certain situations, favorable for power production, it does not exceed 1/2.

The phenomenon described by our title should surprise no one. What may be surprising though is how easy it is to produce a quantum system with this feature; moreover, that system is one that is often used for the purpose of showing how systems equilibrate. The violation can be variously manifested. In our detailed example, bringing a detuned 2-level system into contact with a monochromatic reservoir does not cause it to relax to the reservoir temperature; rather, the system acquires the reservoir's level-occupation-ratio.

Given a set of variables and the correlations among them, we develop a method for finding clustering among the variables. The method takes advantage of information implicit in higher-order (not just pairwise) correlations. The idea is to define a Potts model whose energy is based on the correlations. Each state of this model is a partition of the variables and a Monte Carlo method is used to identify states of lowest energy, those most consistent with the correlations. A set of the 100 or so lowest such partitions is then used to construct a stochastic dynamics (using the adjacency matrix of each partition) whose observable representation gives the clustering. Three examples are studied. For two of them the 3$^\mathrm{rd}$ order correlations are significant for getting the clusters right. The last of these is a toy model of a biological system in which the joint action of several genes or proteins is necessary to accomplish a given process.

The puzzle of the thermodynamic arrow of time reduces to the question of how the universe could have had lower entropy in the past. I show that no special entropy lowering mechanism (or fluctuation) is necessary. As a consequence of expansion, at a particular epoch in the history of the universe a state that was near maximum entropy under the dominant short range forces becomes extremely unlikely, due to a switchover to newly dominant long range forces. This happened at about the time of decoupling, prior to which I make no statement about arrows. The role of cosmology in thermodynamics was first suggested by T. Gold., Comment: For the proceedings of the conference DICE2008, Castiglioncello, Italy

We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an equality, significantly extending several recent results. We further show that achieving zero dissipation in a system implies that detailed balance obtains, and as a consequence there is zero power production. We obtain inequalities for power production under more general circumstances and show that near equilibrium obtaining maximum power production requires dissipation to be of the same order of magnitude.

Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We overcome this difficulty. We show that solutions to the QHJE can be constructed by a simple prescription starting from the propagator of the associated Schroedinger equation. Our result opens the possibility of practical use of quantum Hamilton-Jacobi theory. As an application we develop a surprising relation between operator ordering and the density of paths around a semiclassical trajectory., Comment: 7 pages

The state space for the $N$-spin mean field (SK) spin glass--nominally an $N$-cube--is embedded in a low dimensional continuous space in such a way that metastable and stable phases can easily be discerned, a concept of nearness of configurations defined, and peaks in the Parisi $q$-parameter overlap distribution identified. The dynamical and partly hierarchical interrelation of these phases can be directly imaged., Comment: To appear in Phys. Rev. Lett

The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical since the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically one can identify the degrees of freedom supplying this energy. Nevertheless, the energy input can be calculated without specific reference to those degrees of freedom., Comment: To appear in Phys. Rev. Lett

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an \textit{observable-representation of state space}, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.

Using two methods we show that a quantized discrete breather in a 1-D lattice is stable. One method uses path integrals and compares correlations for a (linear) local mode with those of the quantum breather. The other takes a local mode as the zeroth order system relative to which numerical, cutoff-insensitive diagonalization of the Hamiltonian is performed., Comment: 4 pages, 3 figures

Quantum states of a discrete breather are studied in two ways. One method involves numerical diagonalization of the Hamiltonian, the other uses the path integral to examine correlations in the eigenstates. In both cases only the central nonlinearity is retained. To reduce truncation effects in the numerical diagonalization, a basis is used that involves a quadratic local mode. A similar device is used in the path integral method for deducing localization. Both approaches lead to the conclusion that aside from quantum tunneling the quantized discrete breather is stable., Comment: 33 pages, 20 figures, to appear in J. Chem. Phys

The derivation of the Feynman path integral based on the Trotter product formula is extended to the case where the system is in a magnetic field., Comment: To appear in the American Journal of Physics, 2004

A stochastic dynamics framework for the study of complex systems is presented.

Physical fractals invariably have upper and lower limits for their fractal structure. Berry has shown that a particle sharply confined to a box has a wave function that is fractal both in time and space, with no lower limit. In this article, two idealizations of this picture are softened and a corresponding lower bound for fractality obtained. For a box created by repeated measurements (\`a la the quantum Zeno effect), the lower bound is $\Delta x\sim \Delta t (\hbar/{mL})$ with $\Dt$ the interval between measurements and $L$ is the size of the box. For a relativistic particle, the lower bound is the Compton wavelength, $\hbar/mc$. The key step in deriving both results is to write the propagator as a sum over classical paths.

Millisecond crystal relaxation has been used to explain anomalous decay in doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons. Our model exhibits confinement of mechanical energy released by excitation. Extending the model to long times is justified by its relation to solitons, excitations previously proposed to occur in alkali halides. Soliton damping and observation are also discussed.

Under unitary evolution, systems move gradually from state to state. An unstable atom has amplitude in its original state after many lifetimes ($\tau_L$). But in the laboratory, transitions seem to go instantaneously, as suggested by the term "quantum jump." The problem studied here is whether the "jump" can be assigned a duration, in theory and in experiment. Two characteristic times are defined, jump time ($\tau_J$) and passage time ($\tau_P$). Both use Zeno time, $\tau_Z$, defined in terms of $H$ and its initial state as $\tau_Z \equiv \hbar/\sqrt{<\psi| (H-E_\psi)^2 |\psi>}$, with $E_\psi \equiv <\psi|H|\psi>$. $\tau_J$ is defined in terms of the time needed to slow (\`a la the quantum Zeno effect) the decay: $\tau_J \equiv \tau_Z^2/\tau_L$. It appears in several contexts. It is related to tunneling time in barrier penetration. Its inverse is the bandwidth of the Hamiltonian, in a time-energy uncertainty principle. $\tau_J$ is also an indicator of the duration of the quadratic decay regime in both experiment and in numerical calculations (cf. Fig.~2 of PRA 57,1509 (1998).) The passage time, $\tau_P$, arises from unitary evolution sans interpretation. It is based on a bound of Fleming (Nuov. Cim. 16 A, 232 (1973)): for any $H$ and $\psi$ a system cannot evolve to a state orthogonal to $\psi$ for $t< \tau_P \equiv \pi \tau_Z/2$. By including apparatus in $H$, $\tau_P$ limits the observation of decay according to the quantum measurement ideas proposed in "Time's Arrows and Quantum Measurement," Cambridge U. Press, 1997, thereby allowing an experimental test of these ideas., Comment: To appear in: Time in Quantum Mechanics, edited by J. G. Muga, R. Sala Mayato, and I. L. Egusquiza. Springer-Verlag

The emergence of macroscopic variables can be effected through {\it coarse graining}. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced in the coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation., Comment: To appear in Foundations of Physics, Festschrift for Martin Gutzwiller

It was recently shown \cite{opposite} that systems with opposite thermodynamic arrows of time could have moderate mutual interaction with neither destroying the order of the other. Such interaction includes signaling. Signals, however, may give rise to causal paradoxes, suggesting that "moderate" interaction may be impossible. Using the two-time boundary condition framework, we resolve the paradoxes. In one example, at a macroscopic level, we establish the existence of solutions to the appropriate boundary value problem. This result is extended to a class of microscopic problems. We also produce an example in which microscopic data are given and there is no solution. This is a different kind of resolution: there is no paradox because the events do not happen. Finally we discuss the differences between these cases., Comment: To appear in Physics Letters A

The dynamics of a quantum system undergoing frequent measurements (quantum Zeno effect) is investigated. Using asymptotic analysis, the system is found to evolve unitarily in a proper subspace of the total Hilbert space. For spatial projections, the generator of the "Zeno dynamics" is the Hamiltonian with Dirichlet boundary conditions., Comment: 6 pages

Using symmetric boundary conditions at separated times, I show analytically that both the time ordering of (macroscopic) causality and the direction of entropy increase follow from these boundary conditions. In particular, when the endpoints have low entropy, these arrows of time point away from the ends and toward the middle. Causality in this context means that when perturbations are applied, the effect of the perturbation---the macroscopic change in the system's behavior---is confined to one temporal side of the perturbations. These results hold for both mixing and integrable systems, although relaxation for integrable systems is incomplete. Simulations are presented for purposes of illustration., Comment: For the proceedings of the conference, "Time's Arrows, Quantum Measurements and Superluminal Behavior," Naples, Italy, October 2000. To be published by the Italian CNR. Contains two three-part figures

The second law of thermodynamics - the usual statement of the arrow of time - has been called the most fundamental law of physics. It is thus difficult to conceive that a single dynamical system could contain subsystems, in significant mutual contact, possessing opposite thermodynamic arrows of time. By examining cosmological justification for the usual arrow it is found that a consistent way to establish such justification is by giving symmetric boundary conditions at two (cosmologically remote) times and seeking directional behavior in between. Once this has been demonstrated, it is seen that entropy increase can be reversed and that the usual arrow is less totalitarian than previously believed. In the same vein, other boundary conditions, modeling shorter periods in the evolution of the cosmos, can be found that allow the simultaneous existence of two thermodynamic arrows, notwithstanding moderate interaction between the systems possessing those arrows. Physical consequences of the existence and detection of opposite-arrow regions are also considered., Comment: For the proceedings of the conference, Equations aux Derivees Partielles et Physique Mathematique, in honor of J. Vaillant, Paris, June 2000. B. Gaveau et al., editors

This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896 (2000)) on PRL 83, 5419 (1999). The suitability of the particlar two-time boundary value problem used in the earlier PRL is argued.

A model in which two weakly coupled systems maintain opposite running thermodynamic arrows of time is exhibited. Each experiences its own retarded electromagnetic interaction and can be seen by the other. The possibility of opposite-arrow systems at stellar distances is explored and a relation to dark matter suggested., Comment: To appear in Phys. Rev. Lett

We exhibit a specific implementation of the creation of geometrical phase through the state-space evolution generated by the dynamic quantum Zeno effect. That is, a system is guided through a closed loop in Hilbert space by means a sequence of closely spaced projections leading to a phase difference with respect to the original state. Our goal is the proposal of a specific experimental setup in which this phase could be created and observed. To this end we study the case of neutron spin, examine the practical aspects of realizing the "projections," and estimate the difference between the idealized projections and the experimental implementation., Comment: 13 pages, 2 figures

We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power-law exponent whose value does not depend in a very direct way on the specific details of the dynamics. This we do by means of the Renormalization Group, a powerful analytic tool for extracting asymptotic behavior of many-body systems, Comment: Accepted for publication in Astronomy & Astrophysics. 10 pages using A&A style file; 2 eps figures

When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave function optimization required to avoid decoherence is also examined., Comment: 10 pages, plain TeX, no figures

The extent to which a given wave function, $\psi$, is entangled is measured by minimizing the norm of $\psi$ minus all possible unentangled functions. This measure is given by the largest eigenvalue of $\psi^\dagger \psi$, considered as an operator. The definition is basis independent., Comment: 4 pages, plain TeX, no figures