Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

Thermodynamics of adiabatic feedback control

We study adaptive control of classical ergodic Hamiltonian systems, where the controlling parameter varies slowly in time and is influenced by system's state (feedback). An effective adiabatic description is obtained for slow variables of the system. A general limit on the feedback induced negative entropy production is uncovered. It relates the quickest negentropy production to fluctuations of the control Hamiltonian. The method deals efficiently with the entropy-information trade off.Comment: 6 pages, 1 figur

Designing optimal discrete-feedback thermodynamic engines

Feedback can be utilized to convert information into useful work, making it an effective tool for increasing the performance of thermodynamic engines. Using feedback reversibility as a guiding principle, we devise a method for designing optimal feedback protocols for thermodynamic engines that extract all the information gained during feedback as work. Our method is based on the observation that in a feedback-reversible process the measurement and the time-reversal of the ensuing protocol both prepare the system in the same probabilistic state. We illustrate the utility of our method with two examples of the multi-particle Szilard engine.Comment: 15 pages, 5 figures, submitted to New J. Phy

Thermodynamical Cost of Accessing Quantum Information

Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics, information science and biology. Recently, it has been realised that information storage and processing based on quantum mechanics can be much more efficient than their classical counterpart. What general bound on storage of quantum information does thermodynamics imply? We show that thermodynamics implies a weaker bound than the quantum mechanical one (the Holevo bound). In other words, if any post-quantum physics should allow more information storage it could still be under the umbrella of thermodynamics.Comment: 3 figure

Thermodynamic efficiency of information and heat flow

A basic task of information processing is information transfer (flow). Here we study a pair of Brownian particles each coupled to a thermal bath at temperature $T_1$ and $T_2$, respectively. The information flow in such a system is defined via the time-shifted mutual information. The information flow nullifies at equilibrium, and its efficiency is defined as the ratio of flow over the total entropy production in the system. For a stationary state the information flows from higher to lower temperatures, and its the efficiency is bound from above by $\frac{{\rm max}[T_1,T_2]}{|T_1-T_2|}$. This upper bound is imposed by the second law and it quantifies the thermodynamic cost for information flow in the present class of systems. It can be reached in the adiabatic situation, where the particles have widely different characteristic times. The efficiency of heat flow|defined as the heat flow over the total amount of dissipated heat|is limited from above by the same factor. There is a complementarity between heat- and information-flow: the setup which is most efficient for the former is the least efficient for the latter and {\it vice versa}. The above bound for the efficiency can be [transiently] overcome in certain non-stationary situations, but the efficiency is still limited from above. We study yet another measure of information-processing [transfer entropy] proposed in literature. Though this measure does not require any thermodynamic cost, the information flow and transfer entropy are shown to be intimately related for stationary states.Comment: 19 pages, 1 figur

Discrete Symmetries and Generalized Fields of Dyons

We have studied the different symmetric properties of the generalized Maxwell's - Dirac equation along with their quantum properties. Applying the parity (\mathcal{P}), time reversal (\mathcal{T}), charge conjugation (\mathcal{C}) and their combined effect like parity time reversal (\mathcal{PT}), charge conjugation and parity (\mathcal{CP}) and \mathcal{CP}T transformations to varius equations of generalized fields of dyons, it is shown that the corresponding dynamical quantities and equations of dyons are invariant under these discrete symmetries. Abstract Key words- parity, time reversal, charge-conjugation, dyons Abstract PACS No.- 14.80 Hv

Optimal strategies in collective Parrondo games

We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic loses, whereas a periodic or random sequence of choices yields a steadily increase of the capital. An explanation of this behavior is given by noting that the short-range maximization of the returns is "killing the goose that laid the golden eggs". A continuous model displaying similar features is analyzed using dynamic programming techniques from control theory.Comment: 4 pages, 6 figures, revised version in published for

Efficacy of Online Training for Improving Camp Staff Competency

Preparing competent staff is a critical issue within the camp community. This quasi-experimental study examined the effectiveness of an online course for improving staff competency in camp healthcare practices among college-aged camp staff and a comparison group (N = 55). We hypothesized that working in camp would increase competency test scores due to opportunities for staff to experientially apply knowledge learned online. Hierarchical linear modeling was used to analyse the cross-level effects of a between-individuals factor (assignment to experimental or comparison group) and within-individual effects of time (pre-test, post-test #1, and post-test #2) on online course test scores. At post-test #2, the difference in average test scores between groups was ~30 points, with the treatment group scoring lower on average than the comparison group. Factors that may have influenced these findings are explored, including fatigue and the limited durability of online learning. Recommendations for research and practice are discussed

Langevin dynamics with dichotomous noise; direct simulation and applications

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen

Probabilities from Entanglement, Born's Rule from Envariance

I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly entangled ``Bell-like'' states can be used to rigorously justify complete ignorance of the observer about the outcome of any measurement on either of the members of the entangled pair. For more general states, envariance leads to Born's rule, $p_k \propto |\psi_k|^2$ for the outcomes associated with Schmidt states. Probabilities derived in this manner are an objective reflection of the underlying state of the system -- they represent experimentally verifiable symmetries, and not just a subjective ``state of knowledge'' of the observer. Envariance - based approach is compared with and found superior to pre-quantum definitions of probability including the {\it standard definition} based on the `principle of indifference' due to Laplace, and the {\it relative frequency approach} advocated by von Mises. Implications of envariance for the interpretation of quantum theory go beyond the derivation of Born's rule: Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {\it environment - induced superselection (einselection) of pointer states}, that was usually derived by an appeal to decoherence. Envariant origin of Born's rule for probabilities sheds a new light on the relation between ignorance (and hence, information) and the nature of quantum states.Comment: Figure and an appendix (Born's rule for continuous spectra) added. Presentation improved. (Comments still welcome...