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Non-equilibrium fluctuation theorems (NFTs) relate work performed on a system as its Hamiltonian varies with time, to equilibrium data of the initial and final states. In a classical context the system energy can be directly measured, while…
Periodic driving is used to operate machines that go from standard macroscopic engines to small non-equilibrium micro-sized systems. Two classes of such systems are small heat engines driven by periodic temperature variations and molecular…
The fluctuation theorem of the Crooks type is studied for thermodynamic nonlinear- multivariate systems. In particular, a bivariate system having a limit cycle is discussed in detail. It is explicitly shown how the time reversal operation…
One of the most important goals in quantum thermodynamics is to demonstrate advantages of thermodynamic protocols over their classical counterparts. For that, it is necessary to (i) develop theoretical tools and experimental set-ups to deal…
The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in last the decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a…
We study the response of dynamical systems to finite amplitude perturbation. A generalized Fluctuation-Response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out…
For diffusive systems that can be described by fluctuating hydrodynamics and by the Macroscopic Fluctuation Theory of Bertini et al., the total current fluctuations display universal features when the system is closed and in equilibrium.…
The fluctuation in electric current in nonequilibrium steady states is investigated by molecular dynamics simulation of macroscopically uniform conductors. At low frequencies, appropriate decomposition of the spectral intensity of current…
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. Their general validity arbitrarily far from equilibrium makes them invaluable in nonequilibrium physics. So far, experimental studies of…
Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The…
The link between forced and free fluctuations for nonequilibrium systems can be described via a generalized version of the celebrated fluctuation-dissipation theorem. The use of the formalism of the Koopman operator makes it possible to…
For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a…
The fluctuation-response relation is a fundamental relation that is applicable to systems near equilibrium. On the other hand, when a system is driven far from equilibrium, this relation is violated in general because the detailed-balance…
The principle of covariance, a cornerstone of modern physics, asserts the equivalence of all inertial frames of reference. Fluctuation theorems, as extensions of the second law of thermodynamics, establish universal connections between…
For current fluctuations in non-equilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any…
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems,…
Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constrained by dissipation. Fluctuation relations generalize the second law of thermodynamics to stochastic processes. We show that any…
The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the fluctuation--dissipation theorem to far from equilibrium…
Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly…
It will be shown, how the Boltzmannian ideas on statistical physics can be naturally applied to nonequilibrium thermodynamics. A similar approach for treating nonequilibrium phenomena has been successfully used by Einstein and Smoluchowski…