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Journal of Physics Conference Series

Thermodynamic and relativistic uncertainty relations

A. A. Artamonov, Evgenii V. Plotnikov

Published Jan 1, 2017• 2 citations
Publisher

Abstract

Thermodynamic uncertainty relation (UR) was verified experimentally. The experiments have shown the validity of the quantum analogue of the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger UR. We have also proposed a new type of UR for the relativistic mechanics. These relations allow us to consider macroscopic phenomena within the limits of the ratio of the uncertainty relations for different physical quantities.

DOI
10.1088/1742-6596/798/1/012098

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Thermodynamic uncertainty relation (UR) was verified experimentally. The experiments have shown the validity of the quantum analogue of the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger UR. We have also proposed a new type of UR for the relativistic mechanics. These relations allow us to consider macroscopic phenomena within the limits of the ratio of the uncertainty relations for different physical quantities.
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.
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.
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.
The paper addresses physics of thermodynamic fluctuations in temperature and energy. These fluctuations are interrelated and, hence, can affect various micro- and macro systems. It is shown that the thermodynamic uncertainty relation must be taken into account in the physics of superconductivity, in quantum computations and other branches of science, where temperature and energy fluctuations play a critical role. One of the most important applications of quantum thermodynamics is quantum computers. It is assumed that in the near future the state structures will create a specific quantum cryptocurrency obtained using quantum computing. The quantum cryptocurrency exhibits two main features: the maximum reliability (quantum protection against hacking threats) and the possibility of state control (at the moment, only large scientific state centers have quantum computers). The paper reviews the studies aimed to theoretically prove the validity of the thermodynamic uncertainty relation. This relation connects fluctuations in temperature and energy of a system. Other similar relations are considered, including the relationship between fluctuations in pressure and volume, in entropy and temperature, and others. The main purpose of the paper is to validate the thermodynamic analogue of the uncertainty relation that interconnects temperature and energy fluctuations. Experimental data was obtained on the basis of the study of the transport properties of semiconductor devices – transistors. In the experiment, the transport properties of a pair of semiconductor transistors placed on a single silicon crystal were studied. In this system, one transistor was used to determine temperature fluctuations, and the other one was employed to estimate energy fluctuations. The key role of the thermodynamic uncertainty relation in modern thermodynamics has been clarified. The performed experimental studies confirm the validity of the thermodynamic uncertainty relation.
This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited mathematical formulas, without any essential significance for physics. Such a finding reinforces the Dirac's prediction that UR "`in their present form will not survive in the physics of future"'. The noted facets of UR motivate reconsiderations of associated debates on QMS. Mainly one reveals that, properly, UR have not any essential connection with genuine descriptions of QMS. For such descriptions, it is necessary that, mathematically, the quantum observables to be considered as random variables. The measuring scenarios with a single sampling, such are wave function collapse or Schrodinger's cat thought experiment, are revealed as being useless exercises. We propose to describe QMS as transmission processes for stochastic data. Note that the above-announced revaluation of UR and QMS philosophy does not disturb in any way the practical framework of the usual quantum mechanics.