Related papers: Tsallis statistics generalization of non-equilibri…
Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such…
This chapter reviews an information theoretic approach to deriving quantum fluctuation theorems. When a thermal system is driven from equilibrium, random quantities of work are required or produced: the Crooks equality is a classical…
The Jarzynski equality relates the free energy difference between two equilibrium states to the fluctuating irreversible work afforded to switch between them. The prescribed fixed temperature for the equilibrium states implicitly constrains…
Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…
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 compare two predictions regarding the microscopic fluctuations of a system that is driven away from equilibrium: one due to Crooks [J. Stat. Phys. 90, 1481 (1998)] which has gained recent attention in the context of nonequilibrium work…
The nonequilibrium free energy theorems show how distributions of work along nonequilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way…
Recent progress on micro- and nanometer scale manipulation has opened the possibility to probe systems small enough that thermal fluctuations of energy and coordinate variables can be significant compared with their mean behavior. We…
We present here a set of lecture notes on exact fluctuation relations. We prove the Jarzynski equality and the Crooks fluctuation theorem, two paradigmatic examples of classical fluctuation relations. Finally we consider their quantum…
For classical systems driven out of equilibrium, Crooks derived a relation (the Crooks-Jarzynski relation), whose special cases include a relation (the Crooks relation) equivalent to the Kawasaki non-linear response relation. We derive a…
The Jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control. The new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
In this work, we numerically verify the Jarzynski equality and Crook fluctuation theorem for a Brownian particle diffusing in a heterogeneous thermal bath and hence having a non-Gaussian position distribution. We use the…
It has been shown recently that the Jarzynski equality is generalized under nonequilibrium feedback control [T. Sagawa and M. Ueda, Phys. Rev. Lett. {\bf 104}, 090602 (2010)]. The presence of feedback control in physical systems should…
The characteristic function of the work performed by an external time-dependent force on a Hamiltonian quantum system is identified with the time-ordered correlation function of the exponentiated system's Hamiltonian. A similar expression…
We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating a probability measure-valued process. In order to establish a bridge between microscopic and macroscopic behaviors,…
Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields aninequality that puts a lower bound on the average work…
The Jarzynski relation is a recently discovered result relating the average exponential of the work done under nonequilibrium conditions to an equilibrium free energy difference. We illustrate this remarkable relation by considering the…
The Jarzynski Equality relates the free energy difference between two equilibrium states of a system to the average of the work over all irreversible paths to go from one state to the other. We claim that the derivation of this equality is…
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.