Equilibrium Chemical Engines

An equilibrium reversible cycle with a certain engine to transduce the energy of any chemical reaction into mechanical energy is proposed. The efficiency for chemical energy transduction is also defined so as to be compared with Carnot efficiency. Relevance to the study of protein motors is discussed. KEYWORDS: Chemical thermodynamics, Engine, Efficiency, Molecular machine.Comment: 5 pages, late

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

The Carnot Cycle for Small Systems: Irreversibility and the Cost of Operations

We employ the recently developed framework of the energetics of stochastic processes (called `stochastic energetics'), to re-analyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find that both processes of connection to and disconnection from heat baths and adiabatic processes that cause distortion of the energy distribution are sources of inevitable irreversibility within the cycle. Also, the so-called null-recurrence property of the cumulative efficiency of energy conversion over many cycles and the irreversible property of isolated, purely mechanical processes under external `macroscopic' operations are discussed in relation to the impossibility of a perpetual machine, or Maxwell's demon.Comment: 11 pages with 3 figures. Resubmitted to Physical Review E. Many paragraphs have been modifie

Noninvasive Measurement of Dissipation in Colloidal Systems

According to Harada and Sasa [Phys. Rev. Lett. 95, 130602 (2005)], heat production generated in a non-equilibrium steady state can be inferred from measuring response and correlation functions. In many colloidal systems, however, it is a nontrivial task to determine response functions, whereas details about spatial steady state trajectories are easily accessible. Using a simple conditional averaging procedure, we show how this fact can be exploited to reliably evaluate average heat production. We test this method using Brownian dynamics simulations, and apply it to experimental data of an interacting driven colloidal system

Internal Stress in a Model Elasto-Plastic Fluid

Plastic materials can carry memory of past mechanical treatment in the form of internal stress. We introduce a natural definition of the vorticity of internal stress in a simple two-dimensional model of elasto-plastic fluids, which generates the internal stress. We demonstrate how the internal stress is induced under external loading, and how the presence of the internal stress modifies the plastic behavior.Comment: 4 pages, 3 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

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

Exact results for nucleation-and-growth in one dimension

We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur simultaneously, the island distribution has discontinuous derivatives on the rays x_n(t)=nt, n=1,2,3... We introduce an accelerated growth mechanism where the velocity increases linearly with the island size. We solve for the inter-island gap density and show that the system reaches complete coverage in a finite time and that the near-critical behavior of the system is robust, i.e., it is insensitive to details such as the nucleation mechanism.Comment: 9 pages, revtex, also available from http://arnold.uchicago.edu/~ebn

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