Nonequilibrium driven by an external torque in the presence of a magnetic field

Abstract

We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parameters such as mass, viscosity coefficient, and stiffness of the harmonic potential, and the magnetic field, which is not observed in the overdamped limit. We derive the existence condition for the steady state. We examine the combined influence of the non-conservative force and the magnetic field on non-equilibrium characteristics such as non-Boltzmann steady-state probability distribution function, probability currents, entropy production, position-velocity correlation, and violation of fluctuation-dissipation relation.

Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force

“…As shown in the figure, Q am uv,∞ (W am ) satisfies the bound (20). When A 0 = 0, the numerical data are consistent with our analytic result (56). For all parameter spaces, it seems that Q am uv,∞ (W am ) is a monotonically decreasing function of f 0 and a monotonically increasing function of µ 0 and A 0 .…”

“…As we are interested in the steady state, we need a condition for guaranteeing a stable solution of this linear system which is given by [26,56]…”

“…We remark that the original TUR is valid for all parameter regions when we take the Lorentz force as the irreversible one. In this case, the EP rate includes an extra positive unconventional term σ unc s = 2B 2 (k+κB/γ)/(mγK) [51,56]. However, it is not clear at this moment that this choice may guarantee the validity of the original TUR in a more generalized model with a magetic field as well as nonlinear nonconservative forces.…”

Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force

“…The diagonal elements represent a force applied by a harmonic potential with spring constant k, while the offdiagonal elements indicate a nonequilibrium driving force with strength ǫ. This system has been investigated in various studies [34,37,39,[52][53][54], because it is analytically solvable. In the remaining text, we will omit the subscript η for brevity.…”

Exactly solvable two-terminal heat engine with asymmetric Onsager coefficients: Origin of the power-efficiency bound

“…The two-dimensional version has been studied in various contexts with and without a magnetic field [21][22][23][24][25][26] and the Onsager coefficients turn out to be symmetric even in the presence of a magnetic field (see Appendix A). This is why we resort to a more complicated three-dimensional version, still keeping only two terminals.…”