New aspects in 1/fnoise studies

Exact nonequilibrium work generating function for a small classical system

“…[41] Thus, one has to be quite careful when defining the external work, as that choice can substantially change the final form for any fluctuation relation [9]. Indeed, fluctuation relations that are derived under distinct choices of the definition of work used will lead to distinct forms of the fluctuation theorems [8,9,[11][12][13][14][15][16][17][18][19][20] (FT). The JE have been demonstrated exactly for systems initially thermalized at temperature T , that can be either mechanically closed or in contact with a thermostat (at temperature T also) all the time.…”

Nonequilibrium work equalities in isolated quantum systems

“…Conventional derivations of the classical JE and BKE depend on the definitions of the work [2,3,7], namely, defining the work first and approving it satisfying some equality later. This scheme was also used in quantum regimes [37-40, 47, 48, 53, 54].…”

Random paths and current fluctuations in nonequilibrium statistical mechanics

“…The theory leads to the Levitov-Lesovik formula for the generating function of full counting statistics in electron quantum transport [115][116][117]. By taking successive derivatives with respect to the counting parameters λ λ λ, the Green-Kubo formulas and CasimirOnsager reciprocity relations can be generalized to higher-order responses properties thanks to the current fluctuation theorem [33,34,43,44]. These results are investigated experimentally in mesoscopic electronic circuits [118][119][120][121].…”

“…but also generalizations of these relations to the higher cumulants and the nonlinear response coefficients [30,43,44]. In particular, the nonlinear response coefficients (73) are related to the diffusivities (68) according to…”

“…Nowadays, fluctuation theorems have been proved for all the current flowing across a nonequilibrium system would this latter be quantum or stochastic [28][29][30][31][32][33][34][35][36][37][38]. Moreover, such theorems have been shown to have implications not only in linear response theory where the Green-Kubo formulas and the Onsager reciprocity relations are recovered [39][40][41][42], but also in nonlinear response theory where the generalizations of these classic results have been discovered [28,30,33,34,43,44].…”