Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1211.3017

Squeezed coherent states as thermal-like ones (on the problem of incorporating thermodynamics into quantum theory)

Alexander D. Sukhanov, O. N. Golubjeva, V. G. Baryakhtar

Published Nov 13, 2012• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1211.3017

Related papers

Quantum mechanical analogue of the zeroth law of thermodynamics. (On the problem of incorporating Thermodynamics into Quantum Theory)

O. N. Golubjeva, Alexander D. Sukhanov

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.

arXiv:1303.6105•Mar 25, 2013•0 citations

Quantum-Mechanical Analog of the Zeroth Law of Thermodynamics (to the Problem of Incorporating Thermodynamics into the Quantum-Mechanical Theory)

Alexander D. Sukhanov, O. N. Golubjeva, V. G. Baryakhtar

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.

Ukrainian Journal of Physics•Aug 1, 2013•1 citation

The Schrödinger uncertainty relation as a key tool for incorporating statistical thermodynamics into quantum theory

O. N. Golubjeva, Alexander D. Sukhanov

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.

Canadian Journal of Physics•Oct 22, 2013•1 citation

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

Alexander D. Sukhanov, O. N. Golubjeva

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.

Physics of Particles and Nuclei Letters•May 1, 2012•2 citations

Correlated Coherent States - Quantum Analogue Of Thermal States.(On The Problem Of Incorporating Thermodynamics Into Quantum Theory)

Alexander D. Sukhanov, O. N. Golubjeva, V. G. Baryakhtar

In this paper, we show that correlated coherent states (CCSs) are the most adequate candidates for the role of quantum analogues of the thermal states. The main result of our study reduces to the fact that quantum thermal effects under conditions of the equilibrium of an object with the stochastic environment at any temperatures can be explained consistently only on the basis of the set of CCSs.

arXiv:1211.3900•Nov 16, 2012•0 citations

Quantum thermodynamics under observation : the influence of quantum measurements

Jahnke, Thomas

The rather new field of quantum thermodynamics intends to derive thermodynamics from quantum mechanics, as well as to study thermodynamical behavior of quantum systems. It turns out that, indeed, thermalization can be obtained even for very small quantum systems due to the interaction with an appropriate environment. The consideration of an ensemble, as in statistical mechanics, is not necessary. However, the total system - consisting of system and environment - in quantum thermodynamics is usually considered to be closed. In particular, there exists no interaction with an external observer. Since quantum measurements typically influence the measured system, one may wonder which influence such an observation will have in the quantum thermodynamical setting. In this thesis, we study this influence of measurements in quantum thermodynamical systems. It turns out that various concepts known from statistical mechanics arise from such a "quantum thermodynamics under observation", although they do not have any meaning in the isolated quantum thermodynamical setting. The model discussed in the first part consists of a two-level system coupled to a large spin environment, the magnetization of which is measured periodically. This leads to quasi-classical trajectories for the system and - as in statistical mechanics - thermalization and temperature only have a meaning in terms of an ensemble average or a long-time average. Calculating these averages, we prove the ergodicity of the system. Interestingly, the entropy of the obtained attractor state depends on the time between the measurements and can be shown to be connected with the subjective lack of knowledge of the observer. In case of optimal measurements, the ensemble averaged state of the system under periodic measurements equals the state of the system in the quantum thermodynamical model without measurements. Introducing a detuning between system and environment, we find that the system can be prepared in almost arbitrary thermal states due to the periodic measurements. Even the creation of inversion becomes possible. As shown in numerical simulations, our results, which were analytically obtained for large environments, are even applicable to describe the behavior of the system coupled to small environments consisting of only a few spins. Besides measurements of the environment, we also study direct projective measurements of the system, as well as measurements with finite duration, obtaining that the dynamics of the system is almost independent of the concrete realization of the measurements. In the second part of the thesis, we discuss the meaning of temperature fluctuations in quantum thermodynamical systems. In statistical mechanics, there exist different approaches to the problem of temperature fluctuations, which lead to the well-known temperature fluctuation formula. The nature and operational accessibility of these fluctuations, however, remains rather unclear. We argue that according to quantum thermodynamics a system relaxes into a quasi-stationary thermal state and therefore the temperature does not fluctuate. However, since temperature is not an observable, it can only be determined indirectly. For modular systems, we show that the fluctuations of the temperature estimate obtained from a single energy measurement, indeed, are given by the temperature fluctuation formula derived in statistical mechanics, but only within a certain temperature range. The validity range of this formula increases with increasing size of the system. Thus, one can conclude that these "temperature fluctuations" can be interpreted as representing a fundamental limit for the instantaneous determination of temperature.

•Jan 1, 2011•0 citations
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.
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.
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 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.
The rather new field of quantum thermodynamics intends to derive thermodynamics from quantum mechanics, as well as to study thermodynamical behavior of quantum systems. It turns out that, indeed, thermalization can be obtained even for very small quantum systems due to the interaction with an appropriate environment. The consideration of an ensemble, as in statistical mechanics, is not necessary. However, the total system - consisting of system and environment - in quantum thermodynamics is usually considered to be closed. In particular, there exists no interaction with an external observer. Since quantum measurements typically influence the measured system, one may wonder which influence such an observation will have in the quantum thermodynamical setting. In this thesis, we study this influence of measurements in quantum thermodynamical systems. It turns out that various concepts known from statistical mechanics arise from such a "quantum thermodynamics under observation", although they do not have any meaning in the isolated quantum thermodynamical setting. The model discussed in the first part consists of a two-level system coupled to a large spin environment, the magnetization of which is measured periodically. This leads to quasi-classical trajectories for the system and - as in statistical mechanics - thermalization and temperature only have a meaning in terms of an ensemble average or a long-time average. Calculating these averages, we prove the ergodicity of the system. Interestingly, the entropy of the obtained attractor state depends on the time between the measurements and can be shown to be connected with the subjective lack of knowledge of the observer. In case of optimal measurements, the ensemble averaged state of the system under periodic measurements equals the state of the system in the quantum thermodynamical model without measurements. Introducing a detuning between system and environment, we find that the system can be prepared in almost arbitrary thermal states due to the periodic measurements. Even the creation of inversion becomes possible. As shown in numerical simulations, our results, which were analytically obtained for large environments, are even applicable to describe the behavior of the system coupled to small environments consisting of only a few spins. Besides measurements of the environment, we also study direct projective measurements of the system, as well as measurements with finite duration, obtaining that the dynamics of the system is almost independent of the concrete realization of the measurements. In the second part of the thesis, we discuss the meaning of temperature fluctuations in quantum thermodynamical systems. In statistical mechanics, there exist different approaches to the problem of temperature fluctuations, which lead to the well-known temperature fluctuation formula. The nature and operational accessibility of these fluctuations, however, remains rather unclear. We argue that according to quantum thermodynamics a system relaxes into a quasi-stationary thermal state and therefore the temperature does not fluctuate. However, since temperature is not an observable, it can only be determined indirectly. For modular systems, we show that the fluctuations of the temperature estimate obtained from a single energy measurement, indeed, are given by the temperature fluctuation formula derived in statistical mechanics, but only within a certain temperature range. The validity range of this formula increases with increasing size of the system. Thus, one can conclude that these "temperature fluctuations" can be interpreted as representing a fundamental limit for the instantaneous determination of temperature.