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

Universal efficiency at optimal work with Bayesian statistics

If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a) \propto 1/a^{\gamma}$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes' theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a new connection between thermodynamic behavior and the concept of information.Comment: revtex4, 5 pages, abstract changed and presentation improved; results unchanged. New result with Bayes Theorem adde

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

Information erasure without an energy cost

Landauer argued that the process of erasing the information stored in a memory device incurs an energy cost in the form of a minimum amount of mechanical work. We find, however, that this energy cost can be reduced to zero by paying a cost in angular momentum or any other conserved quantity. Erasing the memory of Maxwell's demon in this way implies that work can be extracted from a single thermal reservoir at a cost of angular momentum and an increase in total entropy. The implications of this for the second law of thermodynamics are assessed.Comment: 8 pages with 1 figure. Final published versio

Hamiltonian Derivations of the Generalized Jarzynski Equalities under Feedback Control

In the presence of feedback control by "Maxwell's demon," the second law of thermodynamics and the nonequilibrium equalities such as the Jarzynski equality need to be generalized. In this paper, we derive the generalized Jarzynski equalities for classical Hamiltonian dynamics based on the Liouville's theorem, which is the same approach as the original proof of the Jarzynski equality [Phys. Rev. Lett. 78, 2690 (1997)]. The obtained equalities lead to the generalizations of the second law of thermodynamics for the Hamiltonian systems in the presence of feedback control.Comment: Proceedings of "STATPHYS - Kolkata VII", November 26-30, 2010, Kolkata, Indi

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

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

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

Efficiency of a Brownian information machine

A Brownian information machine extracts work from a heat bath through a feedback process that exploits the information acquired in a measurement. For the paradigmatic case of a particle trapped in a harmonic potential, we determine how power and efficiency for two variants of such a machine operating cyclically depend on the cycle time and the precision of the positional measurements. Controlling only the center of the trap leads to a machine that has zero efficiency at maximum power whereas additional optimal control of the stiffness of the trap leads to an efficiency bounded between 1/2, which holds for maximum power, and 1 reached even for finite cycle time in the limit of perfect measurements.Comment: 9 pages, 2 figure

Energy Requirement of Control: Comments on Szilard's Engine and Maxwell's Demon

In mathematical physical analyses of Szilard's engine and Maxwell's demon, a general assumption (explicit or implicit) is that one can neglect the energy needed for relocating the piston in Szilard's engine and for driving the trap door in Maxwell's demon. If this basic assumption is wrong, then the conclusions of a vast literature on the implications of the Second Law of Thermodynamics and of Landauer's erasure theorem are incorrect too. Our analyses of the fundamental information physical aspects of various type of control within Szilard's engine and Maxwell's demon indicate that the entropy production due to the necessary generation of information yield much greater energy dissipation than the energy Szilard's engine is able to produce even if all sources of dissipation in the rest of these demons (due to measurement, decision, memory, etc) are neglected.Comment: New, simpler and more fundamental approach utilizing the physical meaning of control-information and the related entropy production. Criticism of recent experiments adde