Asymmetry relations and effective temperatures for biased Brownian gyrators

Abstract

We focus on a paradigmatic two-dimensional model of a nanoscale heat engine, - the so-called Brownian gyrator - whose stochastic dynamics is described by a pair of coupled Langevin equations with different temperature noise terms. This model is known to produce a curl-carrying non-equilibrium steady-state with persistent angular rotations. We generalize the original model introducing constant forces doing work on the gyrator, for which we derive exact asymmetry relations, that are reminiscent of the standard fluctuation relations. Unlike the latter, our relations concern instantaneous and not time averaged values of the observables of interest. We investigate the full two-dimensional dynamics as well as the dynamics projected on the $x$- and $y$-axes, so that information about the state of the system can be obtained from just a part of its degrees of freedom. Such a state is characterized by effective "temperatures" that can be measured in nanoscale devices, but do not have a thermodynamic nature. Remarkably, the effective temperatures appearing in full dynamics are distinctly different from the ones emerging in its projections, confirming that they are not thermodynamic quantities, although they precisely characterize the state of the system.

arXiv comment6 pages, 1 figure

References in corpus (27)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Dynamical ensembles in stationary states
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• The effective temperature
• Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• On the heat flux and entropy produced by thermal fluctuations
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Non-equilibrium and information: the role of cross-correlations
• Experimental Realization of a Minimal Microscopic Heat Engine
• Nonequilibrium and irreversibility
• Non-equilibrium work relations
• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• Effective thermodynamics for a marginal observer
• Steady state fluctuation relations for systems driven by an external random force
• On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium
• Two-temperature Langevin dynamics in a parabolic potential
• Ergodicity, ensembles, irreversibility in Boltzmann and beyond
• The Steady State Fluctuation Relation for the Dissipation Function
• Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations
• Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
• Two-temperature Brownian dynamics of a particle in a confining potential
• Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux
• A simple system with two temperatures
• On the relaxation to nonequilibrium steady states
• Theoretical description of effective heat transfer between two viscously coupled beads

Cited by in corpus (20)

• Integral Fluctuation Relations for Entropy Production at Stopping Times
• How irreversible are steady-state trajectories of a trapped active particle?
• Engineered Swift Equilibration of a Brownian Gyrator
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Inertial effects on the Brownian gyrator
• An autonomous out of equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations
• Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator
• Proposal of a realistic stochastic rotor engine based on electron shuttling
• Variance sum rule: proofs and solvable models
• Current-mediated synchronization of a pair of beating non-identical flagella
• Fractional Brownian Gyrator
• Information Arbitrage in Bipartite Heat Engines
• Cooperative dynamics in two-component out-of-equilibrium systems: Molecular "spinning tops"
• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Destructive effect of fluctuations on the performance of a Brownian gyrator
• Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes
• Irregular gyration of a two-dimensional random-acceleration process in a confining potential
• Force-free kinetic inference of entropy production
• Brownian magneto-gyrator as a tunable microengine
• Anisotropic thermalization propelled motor