Extended Nyquist formula for a resistance subject to a heat flow

Abstract

The Nyquist formula quantifies the thermal noise driven fluctuations of voltage across a resistance in equilibrium. We deal here with the case of a resistance driven out of equilibrium by putting it in contact with two thermostats at different temperatures. We reach a non-equilibrium steady state where a heat flux is flowing through the resistance. Our measurements demonstrate anyway that a simple extension of the Nyquist formula to the non uniform temperature field describes with an excellent precision the thermal noise. For a metallic ohmic material, the fluctuations are actually equivalent to those of a resistance in equilibrium with a single thermostat at the mean temperature between the hot and cold sources.

Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation

“…This possibly simplifies the design of the system which does not need to be kept at a single low temperature. Applications may comprehend: noise in nano-mechanical resonators [20] can be predicted when the system is subject to a temperature gradient; gravitational waves detection in cryogenic conditions is now at the testing phase [21], and the out of equilibrium state of the suspended mirrors has to be taken into account [19]; Johnson noise can be modeled through the proposed description when a ΔT is applied [8]; the quest for ultra stable oscillators with cryogenic quartz micro resonators [22]. Furthermore, experiments such as the aforementioned are necessary to test the validity of the latest theoretical predictions over fluctuation theorems and the relative inequalities [23].…”

“…In many applications, however, equilibrium is not a given. In living systems [6], aging materials [7] and systems subject to a heat flux [8,9], for example, the FDT cannot be expected to hold a priori, and such aforementioned experiments are then necessary to test its validity beyond the thermodynamic equilibrium hypotheses. In many cases higher fluctuations with respect to equilibrium are measured when out of equilibrium, thus violating the FDT [9][10][11].…”

Stochastic thermodynamics: experiment and theory

“…• Monnet et al generalize Nyquist's 1928 expression for the voltage fluctuations across a resistor at constant temperature (Johnson noise) to the case of a resistor whose two ends contact two thermal reservoirs with different temperatures. Experiments agree with a simple theory that predicts that in a nonequilibrium steady state, the fluctuations are equivalent to an equilibrium system held at the mean temperature of the two thermostats [2]. • Severino et al give a detailed account of how to measure equilibrium free-energy differences between folded and unfolded states of single molecules (DNA and RNA hairpins).…”

Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation

“…As a result, we believe that this procedure can have a broad range of applications, owning to the generality of the underlying method. Possibly noise in nano-mechanical resonators [24] can be predicted when the system is subject to a temperature gradient; gravitational waves detection in cryogenic conditions is now at the testing phase [25], and the out of equilibrium state of the suspended mirrors has to be taken into account [23]; Johnson noise can be modeled through the proposed description when a ∆T is applied [8]. Furthermore, experiments such as the aforementioned are necessary to test the validity of the latest theoretical predictions over fluctuation theorems and the relative inequalities [26].…”