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Physics of Particles and Nuclei Letters

Arbitrary vacuums as a model of stochastic environment: On the problem of incorporating thermodynamics into quantum theory

Alexander D. Sukhanov, O. N. Golubjeva

Published May 1, 2012• 2 citations
Publisher

Abstract

We propose an approach that makes it possible to narrow the gap between the macro- and micro-descriptions of nature (i.e., between thermodynamics and quantum mechanics). This approach is based on introducing the quantum-thermostat model in the form of cold and thermal vacuums. In this case we start from our previously developed microdescription in the form of ( ħ, k ) dynamics instead of the standard quantum mechanics. It is based on using the complex wave function of vacuum. We emphasize the universal role of the stochastic environmental influence in the appearance of correlations between the fluctuations of conjugate parameters on micro- and macrolevels at any temperatures.

DOI
10.1134/s1547477112030120

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We propose an approach that makes it possible to narrow the gap between the macro- and micro-descriptions of nature (i.e., between thermodynamics and quantum mechanics). This approach is based on introducing the quantum-thermostat model in the form of cold and thermal vacuums. In this case we start from our previously developed microdescription in the form of ( ħ, k ) dynamics instead of the standard quantum mechanics. It is based on using the complex wave function of vacuum. We emphasize the universal role of the stochastic environmental influence in the appearance of correlations between the fluctuations of conjugate parameters on micro- and macrolevels at any temperatures.
This approach to the incorporation of stochastic thermodynamics into quantum theory is based on the conception of consistent inclusion of the holistic stochastic environmental influence described by wave functions of the arbitrary vacuum, which was proposed in our paper previously. In this study, we implement the possibility of explicitly incorporating the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger uncertainty relation into quantum theory. This allows comparatively analyzing the sets of states of arbitrary vacuums, namely, squeezed coherent states (SCSs) and correlated coherent states (CCSs). In addition, we compare the results of the construction of stochastic thermodynamics using SCSs and TCCSs with the versions involving the incorporation of thermodynamics into quantum theory developed previously and based on thermofield dynamics and quantum statistical mechanics.
In our paper [1], we proposed an original approach to the incorporation of stochastic thermodynamics into quantum theory. It is based on the concept of consistent inclusion of the holistic stochastic environmental influence modeled by arbitrary Bogoliubov vacua. In our study, we implement a possibility of describing the states of the system "an object + arbitrary vacuum" based on the wave function. The fact that the quantum language is required becomes especially appreciable in the cases where thermal and quantum fluctuations occur simultaneously. This allows analyzing different types of quantum states and estimating the degree of their applicability to the description of thermal effects. The main result of our study reduces to the fact that squeezed coherent state (SCS) cannot be used to consistently explain quantum-thermal effects under conditions of object equilibrium with the stochastic environment at any temperatures.
The presented approach to incorporate the stochastic thermodynamics into the quantum theory is based on the idea, proposed earlier by the authors, to consistently consider the stochastic influence by the environment considered as the whole and described by the wave functions of arbitrary vacua. In this research, a possibility of the explicit incorporation of the zeroth law of stochastic thermodynamics into the quantum-mechanical theory in the form of the saturated Schr¨odinger uncertainty relation is realized. This allows a comparative analysis between the sets of arbitrary vacuum states, namely, squeezed coherent (SCSs) and correlated coherent (CCSs) states, to be carried out. A possibility to establish a relation between SCSs and CCSs, on the one hand, and thermal states, on the other hand, is discussed.
We use the concept of consistent describing of the holistic stochastic environmental action on the basis of complex wave functions of the arbitrary vacuum and operators of quantum and thermal influence. In this study, we implement the possibility of explicitly incorporating the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger uncertainty relation into quantum theory. This allows comparatively analyzing the sets of states of arbitrary vacuums, which can be used for the description of thermal equilibrium states.
We suggest a more general than quantum statistical mechanics (QSMQSMQSM) microdescription of objects in a heat bath taken into account a vacuum as an object environment - modification of quantum mechanics at finite temperatures; we call it (ℏ,k)(\hbar, k)(ℏ,k)-dynamics ($ \hbar kD$). This approach allows us in a new manner to calculate some important macroparameters and to modify standard thermodynamics. We create an effective apparatus for features description of nearly perfect fluids in various mediums. As an essentially new model of an object environment we suppose a quantum heat bath and its properties, including cases of cold and warm vacuums, are studied. We describe the thermal equilibrium state in place of the traditional density operator in term of a wave function the amplitude and phase of which have temperature dependence. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the microdescription. We demonstrate that a new macroparameter, namely the effective action, can be obtained through averaging of the Schroedingerian over the temperature dependent wave function. It is established that such different parameters as internal energy, effective temperature, and effective entropy and their fluctuations can be expressed through a single quantity - the effective action.
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.