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We show that the dissipation rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. Namely, for rare processes we prove the fundamental tradeoff $langle dot S_text{e} rangle mathcal{T} geq k_{text{B}} $ between the entropy flow $langle dot S_text{e} rangle$ into the reservoirs and the mean time $mathcal{T}$ to complete a process. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.
In order to perform numerical simulations of the KPZ equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf--Cole transformation applied to a dif
The shear stress relaxation modulus $G(t)$ may be determined from the shear stress $tau(t)$ after switching on a tiny step strain $gamma$ or by inverse Fourier transformation of the storage modulus $G^{prime}(omega)$ or the loss modulus $G^{primeprim
The thermodynamic uncertainty relation (TUR) for underdamped dynamics has intriguing problems while its counterpart for overdamped dynamics has recently been derived. Even for the case of steady states, a proper way to match underdamped and overdampe
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems, e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suita
We have investigated the validity of the fluctuation-dissipation theorem (FDT) and the applicability of the concept of effective temperature in a number of non-equilibrium soft glassy materials. Using a combination of passive and active microrheology