Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components

Sara Cerasoli; Victor Dotsenko; Gleb Oshanin; Lamberto Rondoni

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arXiv · 2011.03124

Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components

Sara Cerasoli·Victor Dotsenko·Gleb Oshanin·Lamberto Rondoni

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Abstract

We consider a model of a two-dimensional molecular machine - called Brownian gyrator - that consists of two coordinates coupled to each other and to separate heat baths at temperatures respectively $T_x$ and $T_y$. We consider the limit in which one component is passive, because its bath is "cold", $T_x \to 0$, while the second is in contact with a "hot" bath, $T_y > 0$, hence it entrains the passive component in a stochastic motion. We derive an asymmetry relation as a function of time, from which time dependent effective temperatures can be obtained for both components. We find that the effective temperature of the passive element tends to a constant value, which is a fraction of $T_y$, while the effective temperature of the driving component grows without bounds, in fact exponentially in time, as the steady-state is approached.

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Sara Cerasoli, Victor Dotsenko, Gleb Oshanin, Lamberto Rondoni. 2020-11-05. Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components. https://arxiv.org/abs/2011.03124

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