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

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

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.

Microscopic heat from the energetics of stochastic phenomena

The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can be removed by adding to these quantities the reversible heat associated with the mesoscopic free energy.Comment: 4 pages, 0 figur

Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential

We study the motion of an overdamped colloidal particle in a time-dependent non-harmonic potential. We demonstrate the first law-like balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy

Energetics of Forced Thermal Ratchet

Molecular motors are known to have the high efficiency of energy transformation in the presence of thermal fluctuation. Motivated by the surprising fact, recent studies of thermal ratchet models are showing how and when work should be extracted from non-equilibrium fluctuations. One of the important finding was brought by Magnasco where he studied the temperature dependence on the fluctuation-induced current in a ratchet (multistable) system and showed that the current can generically be maximized in a finite temperature. The interesting finding has been interpreted that thermal fluctuation is not harmful for the fluctuation-induced work and even facilitates its efficiency. We show, however, this interpretation turns out to be incorrect as soon as we go into the realm of the energetics [Sekimoto,J.Phys.Soc.Jpn.66,1234-1237(1997)]: the efficiency of energy transformation is not maximized at finite temperature, even in the same system that Magnasco considered. The maximum efficiency is realized in the absence of thermal fluctuation. The result presents an open problem whether thermal fluctuation could facilitate the efficiency of energetic transformation from force-fluctuation into work.Comment: 3pages, 4sets of figure

Molecular Chemical Engines: Pseudo-Static Processes and the Mechanism of Energy Transduction

We propose a simple theoretical model for a molecular chemical engine that catalyzes a chemical reaction and converts the free energy released by the reaction into mechanical work. Binding and unbinding processes of reactant and product molecules to and from the engine are explicitly taken into account. The work delivered by the engine is calculated analytically for infinitely slow (``pseudo-static'') processes, which can be reversible (quasi-static) or irreversible, controlled by an external agent. It is shown that the work larger than the maximum value limited by the second law of thermodynamics can be obtained in a single cycle of operation by chance, although the statistical average of the work never exceeds this limit and the maximum work is delivered if the process is reversible. The mechanism of the energy transductionis also discussed.Comment: 8 pages, 3 figues, submitted to J. Phys. Soc. Jp