Thermodynamic uncertainty relation as a fundamental aspect of quantum thermodynamics

Abstract

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 quantumcomputing. 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 relationshipbetween 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.