Energetics of Open Systems and Chemical Potential From Micro-Dynamics Viewpoints

We present the energetic aspect of open systems which may exchange particles with their environments. Our attention shall be paid to the scale that the motion of the particles is described by the classical Langevin dynamics. Along a particular realization of the stochastic process, we study the energy transfer into the open system from the environments. We are able to clarify how much energy each particle carries when it enters or leaves the system. On the other hand, the chemical potential should be considered as the concept in macro scale, which is relevant to the free energy potential with respect to the number of particles. Keywords: open systems, stochastic energetics, chemical potentialComment: 7 pages, 1 figur

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

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

Sum rule for response function in nonequilibrium Langevin systems

We derive general properties of the linear response functions of nonequilibrium steady states in Langevin systems. These correspond to extension of the results which were recently found in Hamiltonian systems [A. Shimizu and T. Yuge, J. Phys. Soc. Jpn. {\bf 79}, 013002 (2010)]. We discuss one of the properties, the sum rule for the response function, in particular detail. We show that the sum rule for the response function of the velocity holds in the underdamped case, whereas it is violated in the overdamped case. This implies that the overdamped Langevin models should be used with great care. We also investigate the relation of the sum rule to an equality on the energy dissipation in nonequilibrium Langevin systems, which was derived by Harada and Sasa.Comment: 8 page

Fluctuation relations for a driven Brownian particle

We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski and Gallavotti-Cohen in different special cases

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

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

A detection of ill-formed patterns about programming style

Programming style plays an important role in program understanding andmaintenance. We have implemented a plan recognition system for source code search,and have attempted detection of ill-formed patterns about programming style through it. In this paper, we present experimental result obtained from a prototype system. Weascertained that our system is able to diagnose various items about programming style,so it may be used as an effective tool of programming style diagnosis.ArticleKnowledge-based software engineering : proceedings of the Third Joint Conference on Knowledge-based Software Engineering in Smolenice, Slovakia, 1998. 165-168 (1998)conference pape