Abstract
The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems: (i) The Clausius inequality does not hold when the system and environment are initially correlated - a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g. in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds we use them to detect unaccounted heat leaks and weak feedback operations ("Maxwell's demons") that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlation for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities and more.
Highlights
Recent years have seen a surge of interest in the thermodynamics of small systems
We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables
II, we introduce the notion of global passivity and use it to derive a version of the Clausius inequality that is valid in the presence of initial system-environment correlation
Summary
Recent years have seen a surge of interest in the thermodynamics of small systems. Classical thermodynamics was developed for macroscopic systems that are weakly coupled to large environments. Because of the microscopic size of the small environments, the interaction with the system will in general modify them, and they can substantially deviate from their initial Gibbs state They may develop a strong correlation to the system of interest. A microbath with very small heat capacity (e.g., several spins) is initially prepared in a thermal state and coupled to a system in a nonthermal state In such scenarios the dynamics is highly non-Markovian and, in addition, the unitary transformation that generates the interactions may add or remove energy from the system-environment setup. We exemplify the use of these new inequalities for detecting unaccounted heat leaks, for detecting the presence of “lazy” Maxwell demons, and for studying the buildup of system-environment correlation in a dephasing scenario In these examples, the results obtained from global passivity are much more useful compared to the standard second law.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
