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