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The Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external…

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…

We develop non-equilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in non-ergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate…

We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time dependent control parameter, the environment is…

Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with…

The interest in active matter stimulates the need to generalize thermodynamic description and relations to active matter systems, which are intrinsically out of equilibrium. One important example is the Jarzynski relation, which links the…

There are two related theorems which hold even in far from equilibrium, namely fluctuation theorem and Jarzynski equality. Fluctuation theorem states the existence of symmetry of fluctuation of entropy production, while Jarzynski equality…

Breakdown of time-reversal symmetry is a defining property of non-equilibrium systems, such as active matter, which is composed of units that consume energy. We employ a formalism that allows us to derive a class of identities associated…

We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together…

Fluctuation relations are derived in systems where the spin degree of freedom and magnetic interactions play a crucial role. The form of the non-equilibrium fluctuation theorems relies in the assumption of a local balance condition. We…

For non-equilibrium systems of interacting particles and for interacting diffusions in d dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current…

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…

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 Macroscopic Fluctuating Theory is presented from a practical and self consistent point of view. We take as starting point the assumption that a system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves by a Langevin…

In this paper we present a first-principles analysis of the nonequilibrium work distribution and the free energy difference of a quantum system interacting with a general environment (with arbitrary spectral density and for all…

We derive the differential equation describing the time evolution of the work probability distribution function of a stochastic system which is driven out of equilibrium by the manipulation of a parameter. We consider both systems described…

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond…

Two-state models provide phenomenological descriptions of many different systems, ranging from physics to chemistry and biology. We investigate work fluctuations in an ensemble of two-state systems driven out of equilibrium under the action…

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…

We study a fluctuation relation representing a nonequilibrium equality indicating that the ratio between the distribution of trajectories obtained by exchanging the initial and final positions is characterized by free energy differences for…