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The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated. The first one derives from…
The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the…
Since the first suggestion of the Jarzynski equality many derivations of this equality have been presented in both, the classical and the quantum context. While the approaches and settings greatly differ from one to another, they all appear…
We present a general scheme to obtain work distribution in closed systems under continuous quantum histories of corresponding "power" operator. The scheme is tested by analytically calculating the quantum work distribution for a prototype…
We give a quantum version of the Jarzynski relation between the distribution of work done over a certain time-interval on a system and the difference of equilibrium free energies. The main new ingredient is the identification of work…
In this note, we will discuss how to compactly express and prove the Jarzynski identity for an open quantum system with dissipative dynamics. We will avoid explicitly measuring the work directly, which is tantamount to continuously…
Nonequilibrium work-Hamiltonian connection for a microstate plays a central role in diverse branches of statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.). We show that the change in…
The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to…
The classical Jarzynski equality establishes an exact relation between the stochastic work performed on a system driven out of thermal equilibrium and the free energy difference in a corresponding quasi-static process. This fluctuation…
We develop a mathematical approach to the nonequilibrium work theorem which is traditionally referred to in statistical mechanics as Jarzynski's identity. We suggest a mathematically rigorous formulation and proof of the identity.
The universal quantum work relation connects a functional of an arbitrary observable averaged over the forward process to the free energy difference and another functional averaged over the time-reversed process. Here, we ask the question…
In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum…
We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many…
It has been established that the inclusive work for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and…
A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To…
A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski…
We present a generalization of Jarzynski's Equality, applicable to quantum systems, relating discretized mechanical work and free-energy changes. The theory is based on a step-wise pulling protocol. We find that work distribution functions…
The Jarzynski equality, which relates equilibrium free-energy difference to an average of non-equilibrium work, plays a central role in modern non-equilibrium statistical thermodynamics. In this paper, we study a weaker consequence of this…
The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary timescale, and the corresponding equilibrium free energy difference, is generalized to quantum systems. Using the…
Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions. Key examples are provided by the Crooks and Jarzynski…