Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature

摘要

This work examines the thermodynamic consequences of the repeated partial projection model for coupling aquantum system to an arbitrary series of environments under feedback control. This paper provides observationaldefinitions of heat andwork that can be realized in current laboratory setups. In contrast to other definitions, it usesonly properties of the environment and the measurement outcomes, avoiding references to the “measurement” ofthe central system’s state in any basis. These definitions are consistent with the usual laws of thermodynamicsat all temperatures, while never requiring complete projective measurement of the entire system. It is shownthat the back action of measurement must be counted as work rather than heat to satisfy the second law.Comparisons are made to quantum jump (unravelling) and transition-probability based definitions, many ofwhich appear as particular limits of the present model. These limits show that our total entropy production isa lower bound on traditional definitions of heat that trace out the measurement device. Examining the masterequation approximation to the process at finite measurement rates, we show that most interactions with theenvironment make the system unable to reach absolute zero. We give an explicit formula for the minimumtemperature achievable in repeatedly measured quantum systems. The phenomenon of minimum temperatureoffers an explanation of recent experiments aimed at testing fluctuation theorems in the quantum realm and placesa fundamental purity limit on quantum computers.