1,654 research outputs found
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 and , 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 . 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, 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...
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