Abstract
We propose a definition of externally measurable quantum work in driven systems. Work is given as a quantum observable on a control device which is forcing the system and can be determined without knowledge of the system Hamiltonian $H_\mathcal{S}$. We argue that quantum work fluctuation theorems which rely on the knowledge of $H_\mathcal{S}$ are of little practical relevance, contrary to their classical counterparts. Using our framework, we derive a fluctuation theorem which is operationally accessible and could in principle be implemented in experiments to determine bounds on free energy differences of unknown systems.
Highlights
The classical Jarzynski equality (JE) [1,2] connects the work W performed in nonequilibrium realizations of a driving protocol with the equilibrium free energy difference F by the relation e−βW = e−β F
The JE tells us that, by measuring the work W for many realizations of the protocol, we can obtain F = −1/β ln(ZB/ZA) between the thermal states of HSA and HSB even though the system never reaches the thermal state with respect to the final Hamiltonian
In the second part we look at the conceptual discrepancy between two-point measurement (TPM) schemes and classical work measurements for the determination of free energy differences and motivate how our proposal could overcome these issues
Summary
The classical work values can be determined by measuring an externally applied force along a path. Such a tool is by construction missing in the TPM scheme. In the following we provide a framework which allows one to define work as an external quantum observable on a control system, similar in spirit to the measurement of work in a classical setting This approach allows us to measure work independently of the knowledge of the system Hamiltonian. In the second part we look at the conceptual discrepancy between TPM schemes and classical work measurements for the determination of free energy differences and motivate how our proposal could overcome these issues.
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