Thermal response of nonequilibriumRCcircuits

Abstract

We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady state data. This procedure is closely related to other fluctuationresponse relations based on the knowledge of the steady state probability distribution. As an example, we show that the nonequilibrium heat capacity in general does not correspond to the correlation between the energy of the system and the heat flowing into it. Rather, also non-dissipative aspects are relevant in the nonequilbrium fluctuation response relations.

Interacting Brownian dynamics in a nonequilibrium particle bath

“…with  the probability current of the environment, that vanishes identically in equilibrium. Even though it could be experimentally estimated [48][49][50][51][52], it has been analytically solved only in few simple situations where the stationary distribution is known [28,53,54]. From the identity L = L * +2v ·∇ [28,46,55], where ∇ is the vector of partial derivatives ∂ x k , and L * is the adjoint of L-the forward generator of the dynamics of the environmentone can easily prove:…”

Experiments in Stochastic Thermodynamics: Short History and Perspectives

“…The measurement of the linear response in out-of-equilibrium systems is another very important aspect. Indeed, the new formulations of the fluctuation dissipation relation (FDR) related to the FT are quite useful for this purpose, because they allow the estimation of the response starting from the measurement of fluctuations of different quantities in nonequilibrium steady states (NESSs) [10,[16][17][18][19][20][21]. Within the context of the FDR for out-of-equilibrium states, many studies have been done on the slow relaxation toward equilibrium, such as in aging glasses after a temperature quench [22][23][24].…”

A General Fluctuation–Response Relation for Noise Variations and its Application to Driven Hydrodynamic Experiments

“…(28) via the response functions (27a)-(27b) along with the simplifications sketched above, we find the susceptibility. Note that the term of the time-symmetric part (27b) proportional to ∂ k ∂ i a i , while in general nonzero, disappears for the particular system in question, since two derivatives of the mean drift a = µF = −µκx vanish due to the quadratic potential (4). Experimental data were sampled at constant rate, with a time step ∆t.…”

“…Namely, a (continuous time) thermal response formula devoid of singular terms can be obtained either by an explicit regularization procedure based on functional methods [25] or through a coordinate rescaling which turns noise perturbations into mechanical ones [26]. This formalism was developed for uncorrelated noises and applied to an experiment of a thermally unbalanced RC circuit [19,20], determining its nonequilibrium heat capacitance [4]. However, for example, the scheme described in [26,25] cannot be applied to hydrodynamically coupled particles.…”

“…Pragmatically, a matrix formulation simplifies this last step. In this way, after the previous analysis of nonequilibrium RC circuits [4], we continue the application of a thermal response theory to experimental data. This complements earlier analysis of experiments focused on the mechanical linear response [32,33,31,13].…”