1,964 research outputs found
Relations between Entropies Produced in Nondeterministic Thermodynamic Processes
Landauer's erasure principle is generalized to nondeterministic processes on
systems having an arbitrary number of non-symmetrical logical states. The
condition that the process is applied in the same way, irrespective of the
initial logical state, imposes some restrictions on the individual heat
exchanges associated with each possible transition. The complete set of such
restrictions are derived by a statistical analysis of the phase-space flow
induced by the process. Landauer's erasure principle can be derived from and is
a special case of these.Comment: 12 pages with one figure; a final major revision in presentation;
physical assumptions are clarified no
Memory erasure in small systems
We consider an overdamped nanoparticle in a driven double-well potential as a
generic model of an erasable one-bit memory. We study in detail the statistics
of the heat dissipated during an erasure process and show that full erasure may
be achieved by dissipating less heat than the Landauer bound. We quantify the
occurrence of such events and propose a single-particle experiment to verify
our predictions. Our results show that Landauer's principle has to be
generalized at the nanoscale to accommodate heat fluctuations.Comment: 4 pages, 4 figure
Dissipation: The phase-space perspective
We show, through a refinement of the work theorem, that the average
dissipation, upon perturbing a Hamiltonian system arbitrarily far out of
equilibrium in a transition between two canonical equilibrium states, is
exactly given by , where and are the
phase space density of the system measured at the same intermediate but
otherwise arbitrary point in time, for the forward and backward process.
is the relative entropy of versus
. This result also implies general inequalities, which are
significantly more accurate than the second law and include, as a special case,
the celebrated Landauer principle on the dissipation involved in irreversible
computations.Comment: 4 pages, 3 figures (4 figure files), accepted for PR
Validity of Landauer's principle in the quantum regime
We demonstrate the validity of Landauer's erasure principle in the strong
coupling quantum regime by treating the system-reservoir interaction in a
consistent way. We show that the initial coupling to the reservoir modifies
both energy and entropy of the system and provide explicit expressions for the
latter in the case of a damped quantum harmonic oscillator. These contributions
are related to the Hamiltonian of mean force and dominate in the strong damping
limit. They need therefore to be fully taken into account in any
low-temperature thermodynamic analysis of quantum systems.Comment: 4 pages, 2 figure
Heat Transfer Operators Associated with Quantum Operations
Any quantum operation applied on a physical system is performed as a unitary
transformation on a larger extended system. If the extension used is a heat
bath in thermal equilibrium, the concomitant change in the state of the bath
necessarily implies a heat exchange with it. The dependence of the average heat
transferred to the bath on the initial state of the system can then be found
from the expectation value of a hermitian operator, which is named as the heat
transfer operator (HTO). The purpose of this article is the investigation of
the relation between the HTOs and the associated quantum operations. Since, any
given quantum operation on a system can be realized by different baths and
unitaries, many different HTOs are possible for each quantum operation. On the
other hand, there are also strong restrictions on the HTOs which arise from the
unitarity of the transformations. The most important of these is the Landauer
erasure principle. This article is concerned with the question of finding a
complete set of restrictions on the HTOs that are associated with a given
quantum operation. An answer to this question has been found only for a subset
of quantum operations. For erasure operations, these characterizations are
equivalent to the generalized Landauer erasure principle. For the case of
generic quantum operations however, it appears that the HTOs obey further
restrictions which cannot be obtained from the entropic restrictions of the
generalized Landauer erasure principle.Comment: A significant revision is made; 33 pages with 2 figure
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
Arbitrarily slow, non-quasistatic, isothermal transformations
For an overdamped colloidal particle diffusing in a fluid in a controllable,
virtual potential, we show that arbitrarily slow transformations, produced by
smooth deformations of a double-well potential, need not be reversible. The
arbitrarily slow transformations do need to be fast compared to the barrier
crossing time, but that time can be extremely long. We consider two types of
cyclic, isothermal transformations of a double-well potential. Both start and
end in the same equilibrium state, and both use the same basic operations---but
in different order. By measuring the work for finite cycle times and
extrapolating to infinite times, we found that one transformation required no
work, while the other required a finite amount of work, no matter how slowly it
was carried out. The difference traces back to the observation that when time
is reversed, the two protocols have different outcomes, when carried out
arbitrarily slowly. A recently derived formula relating work production to the
relative entropy of forward and backward path probabilities predicts the
observed work average.Comment: 6 pages, 6 figure
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
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
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
- …