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The Journal of Chemical Physics

Properties of a macroscopic system as a thermal bath

Alberto Suárez, R. Silbey

Published Dec 15, 1991• 44 citations
Publisher

Abstract

A macroscopic system acting as a heat reservoir affords a simplified description in terms of a collection of independent modes. Although in most cases this model is unable to account for the behavior of the macroscopic system itself, it provides a consistent desciption of the macroscopic degrees of freedom acting as a dissipation mechanism for a microscopic system. This is found to be a consequence of the statistical properties of bath quantities relevant to the dynamics of the microscopic system. Furthermore, these properties ensure that the unphysical features of the independent bath model do not affect its performance as a heat reservoir.

DOI
10.1063/1.461190

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A macroscopic system acting as a heat reservoir affords a simplified description in terms of a collection of independent modes. Although in most cases this model is unable to account for the behavior of the macroscopic system itself, it provides a consistent desciption of the macroscopic degrees of freedom acting as a dissipation mechanism for a microscopic system. This is found to be a consequence of the statistical properties of bath quantities relevant to the dynamics of the microscopic system. Furthermore, these properties ensure that the unphysical features of the independent bath model do not affect its performance as a heat reservoir.
Abstract A model for the thermodynamics of a quantum heat bath is introduced. Under the assumption that the bath molecules have finitely many degrees of freedom and are weakly interacting, we present a general derivation of the equation of state of the bath in the thermodynamic limit. The relation between the temperature and the specific energy of the bath depends on (i) the spectral properties of the molecules, and (ii) the choice of probability measure on the state space of a representative molecule. The results obtained illustrate how the microscopic features of the molecular constituents determine the macroscopic thermodynamic properties of the bath. Our findings can thus be used to compare the merits of different hypotheses for the equilibrium states of quantum systems. Two examples of plausible choices for the probability measure are considered in detail.
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We show that the quantum statistical mechanics (QSM) describing quantum and thermal properties of objects has only the sense of a particular semiclassical approximation. We propose a more general (than QSM) micro description of objects in a heat bath taken into account a vacuum as an object environment; we call it ( ħ, k )-dynamics ( ħkD ). We construct a new model of thermostat, namely, a quantum heat bath and study its properties including the cases of a “cold” and “thermal” vacua. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the determination such macro-quantities as internal energy, effective temperature, and effective entropy. We establish that in ħkD the ratio of effective action to effective entropy at zero temperature equals the universal constant ħ /2 k . This result corresponds to experimental data taken recently under studying of a new matter state—nearly perfect fluid.
We study the behavior of two weakly coupled quantum systems, described by a separable density operator. One of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators, which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism and suitably redefining the vacuum of the macroscopic system. As applications, we study an oscillator interacting with a set of boson oscillators at finite temperature, usually employed in quantum mechanics to describe a Brownian particle; and investigate the behavior of an oscillator in the presence of a heat bath consisting of a set of fermion oscillators.
A recently suggested simple model of an open microscopic system interacting with a bath and behaving like an isothermal Maxwell daemon is simplified and treated numerically. Results obtained confirm expectations that the system can, at the cost of thermal energy of the bath, spontaneously and in a cyclic process, pump particles from a particle reservoir to states with even higher energy. This contradicts the usual opinion based on the second law of macroscopic thermodynamics. For this effect, the interaction with the bath cannot be treated as weak. The role of dephasing owing to this interaction is illustrated.
The process of diffusion constitutes the dissipative motion of a classical particle or group of particles subjected to many-body interactions with their surroundings. When the surroundings consist of an infinitely large system that can rapidly recover from any deviation from thermal equilibrium such that its temperature remains roughly uniform, the system qualifies as a heat bath. Further, when the degrees of freedom of the heat bath are integrated out because of the implied timescale separation, the dynamics of the subsystem appear dissipative, characterized by parameters such as friction coefficient, diffusion constant, and others.