Complementarity relation for irreversible process derived from stochastic energetics

When the process of a system in contact with a heat bath is described by classical Langevin equation, the method of stochastic energetics [K. Sekimoto, J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of Helmholtz free energy and the dissipation function of the system. We prove that the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min, where S_min depends on the initial and the final values of the control parameters, but it does not depend on the pathway between these values.Comment: 3 pages. LaTeX with 6 style macro

Jarzynski equality for the transitions between nonequilibrium steady states

Jarzynski equality [Phys. Rev. E {\bf 56}, 5018 (1997)] is found to be valid with slight modefication for the transitions between nonequilibrium stationary states, as well as the one between equilibrium states. Also numerical results confirm its validity. Its relevance for nonequilibrium thermodynamics of the operational formalism is discussed.Comment: 5 pages, 2 figures, revte

Inattainability of Carnot efficiency in the Brownian heat engine

We discuss the reversibility of Brownian heat engine. We perform asymptotic analysis of Kramers equation on B\"uttiker-Landauer system and show quantitatively that Carnot efficiency is inattainable even in a fully overdamping limit. The inattainability is attributed to the inevitable irreversible heat flow over the temperature boundary.Comment: 5 pages, to appear in Phys. Rev.

Brownian Motors driven by Particle Exchange

We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium states. As an application of the proposed evolution rule, we devise a simple model of Brownian motors driven by particle exchange. KEYWORDS: Langevin Dynamics, Thermodynamics, Open SystemsComment: 5 pages, late

Steady State Thermodynamics of Langevin Systems

We study Langevin dynamics describing nonequilibirum steady states. Employing the phenomenological framework of steady state thermodynamics constructed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf130}, 29 (1998)], we find that the extended form of the second law which they proposed holds for transitions between steady states and that the Shannon entropy difference is related to the excess heat produced in an infinitely slow operation. A generalized version of the Jarzynski work relation plays an important role in our theory.Comment: 4 page

History Memorized and Recalled upon Glass Transition

The memory effect upon glassification is studied in the glass to rubber transition of vulcanized rubber with the strain as a controlling parameter. A phenomenological model is proposed taking the history of the temperature and the strain into account, by which the experimental results are interpreted. The data and the model demonstrate that the glassy state memorizes the time-course of strain upon glassification, not as a single parameter but as the history itself. The data also show that the effect of irreversible deformation in the glassy state is beyond the scope of the present model. Authors' remark: The title of the paper in the accepted version is above. The title appeared in PRL is the one changed by a Senior Assistant Editor after acceptance of the paper. The recovery of the title was rejected in the correction process.Comment: 4 pages, 4 figure

Brownian Carnot engine

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of microscopic Carnot engines is still lacking. Here we report on an experimental realization of a Carnot engine with a single optically trapped Brownian particle as working substance. We present an exhaustive study of the energetics of the engine and analyze the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency -an insight that could inspire novel strategies in the design of efficient nano-motors.Comment: 7 pages, 7 figure

Entropy Production of Brownian Macromolecules with Inertia

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such open systems can have a negative entropy production rate and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external forces, which includes a transverse Lorentz force, leading to equilibrium.Comment: 10 pages, 1 figur

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.Comment: 9 page

Propagation of a Solitary Fission Wave

Reaction-diffusion phenomena are encountered in an astonishing array of natural systems. Under the right conditions, self stabilizing reaction waves can arise that will propagate at constant velocity. Numerical studies have shown that fission waves of this type are also possible and that they exhibit soliton like properties. Here, we derive the conditions required for a solitary fission wave to propagate at constant velocity. The results place strict conditions on the shapes of the flux, diffusive, and reactive profiles that would be required for such a phenomenon to persist, and this condition would apply to other reaction diffusion phenomena as well. Numerical simulations are used to confirm the results and show that solitary fission waves fall into a bistable class of reaction diffusion phenomena. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729927]United States Nuclear Regulatory Commission NRC-38-08-946Mechanical Engineerin