Abstract
We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics. By including a work system whose energy is allowed to fluctuate, we derive a set of equalities which all thermodynamical transitions have to satisfy. This extends the condition for maps to be Gibbs-preserving to the case of fluctuating work, providing a more general characterisation of maps commonly used in the information theoretic approach to thermodynamics. For final states, block diagonal in the energy basis, this set of equalities are necessary and sufficient conditions for a thermodynamical state transition to be possible. The conditions serves as a parent equation which can be used to derive a number of results. These include writing the second law of thermodynamics as an equality featuring a fine-grained notion of the free energy. It also yields a generalisation of the Jarzynski fluctuation theorem which holds for arbitrary initial states, and under the most general manipulations allowed by the laws of quantum mechanics. Furthermore, we show that each of these relations can be seen as the quasi-classical limit of three fully quantum identities. This allows us to consider the free energy as an operator, and allows one to obtain more general and fully quantum fluctuation relations from the information theoretic approach to quantum thermodynamics.
Highlights
The second law of thermodynamics governs what state transformations are possible regardless of the details of the interactions
We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics
This extends the condition for maps to be Gibbs preserving to the case of fluctuating work, providing a more general characterization of maps commonly used in the information theoretic approach to thermodynamics
Summary
The second law of thermodynamics governs what state transformations are possible regardless of the details of the interactions. Able to get a more general classical version of the Jarzynski fluctuation theorem, valid for any initial state, but we are able to derive two fully quantum identities which reduce in the classical limit to these classical generalizations of the Jarzynski equation and the second law. [16] (but with opposite sign convention), J HðρÞ 1⁄4 eðβ=2ÞHρeðβ=2ÞH Some of the other results in Ref. [16] can be derived in our framework as well
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.