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We investigate the nonequilibrium stationary state (NESS) of the two-dimensional Ising model under a stochastic dichotomous modulation of temperature, which alternates between T c ± δ around the critical temperature T c at a rate γ . Both magnetisation and energy exhibit non-monotonic dependence on γ , explained by a renewal approach in the slow-switching limit, while for small δ dynamical response theory quantitatively captures the γ -dependence of the observables. In the fast-switching regime, the NESS appears Boltzmann-like with a γ -dependent effective temperature. However, a finite energy current flowing through the system from hot to cold reservoir confirms the intrinsic nonequilibrium nature of the dynamics.

We discuss the physical meaning and significance of statistical forces on quasi-static probes in first order around detailed balance for driven media. Exploiting the quasi-static energetics and the structure of (McLennan) steady nonequilibrium ensembles, we find that the statistical force obtains a nonequilibrium correction deriving from the excess work of driving forces on the medium in its relaxation after probe displacement. This reformulates, within a more general context, the recent result by Nakagawa (2014 Phys. Rev. E 90 022108) on thermodynamic aspects of weakly nonequilibrium adiabatic pumping. It also proposes a possible operational tool for accessing some excess quantities in steady state thermodynamics. Furthermore, we show that the point attractors of a (macroscopic) probe coupled to a weakly driven medium realize the predictions of the minimum entropy production principle. Finally, we suggest a method to measure the relative dynamical activity through different transition channels, via the measurement of the statistical force induced by a suitable driving.

We present examples of how time-symmetric kinetic factors contribute to the response either in nonlinear order around equilibrium or in linear order around nonequilibrium. The phenomenology we associate to that so called frenetic contribution are negative differential conductivity, changes in the Einstein relation between friction and noise, and population inversion.

Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution.

We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled active Brownian particles, we analytically derive the stationary distribution of the pairwise distances and reveal that the heterogeneity in propulsion speeds induces a characteristic scale of repulsion between particles. This length scale algebraically increases with the difference in their self-propulsion speeds. In contrast to the conventional view that activity in active matter systems typically leads to effective attraction, our results demonstrate that activity can give rise to an emergent repulsive interaction. This phenomenon is universal, independent of the specific dynamics of the particles or the presence of thermal fluctuations. We also discuss possible experimental realization of this counter-intuitive phenomenon.

We study the dynamics of a chirality reversing active Brownian particle, which models the chirality reversing active motion common in many microorganisms and microswimmers. We show that, for such a motion, the presence of the two time-scales set by the chirality reversing rate \\(\\) and rotational diffusion constant \\(D_R\\) gives rise to four dynamical regimes, namely, (I) \\(t min(^-1, D_R^-1)\\), (II) \\(^-1 t D_R^-1\\), (III) \\(D_R^-1 t ^-1\\) and (IV) \\(t max(^-1, D_R^-1)\\), each showing different behaviour. The short-time regime (I) is characterized by a strongly anisotropic and non-Gaussian position distribution, which crosses over to a diffusive Gaussian behaviour in the long-time regime (IV) via an intermediate regime (II) or (III), depending on the relative strength of \\(\\) and \\(D_R\\). In regime (II), the chirality reversing active Brownian motion reduces to that of an ordinary active Brownian particle, with an effective rotation diffusion coefficient which depends on the angular velocity. Finally, we find that, the regime (III) is characterized by an effective chiral active Brownian motion.

We investigate the nonequilibrium stationary state (NESS) of the two-dimensional Ising model under a stochastic dichotomous modulation of temperature, which alternates between \\(T_c \\) around the critical temperature \\(T_c\\) at a rate \\(\\). Both magnetization and energy exhibit non-monotonic dependence on \\(\\), explained by a renewal approach in the slow-switching limit, while for small \\(\\) dynamical response theory quantitatively captures the \\(\\)-dependence of the observables. In the fast-switching regime, the NESS appears Boltzmann-like with a \\(\\)-dependent effective temperature. However, a finite energy current flowing through the system from hot to cold reservoir confirms the intrinsic nonequilibrium nature of the dynamics.

We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent \\(\\). We find that the power-law resetting leads to a rich behaviour for the currents, as well as density profile. We show that, for any finite system, for \\(<1\\), the density profile eventually becomes uniform while for \\( >1\\), an eventual non-trivial stationary profile is reached. We also find that, in the limit of thermodynamic system size, at late times, the average diffusive current grows \\( t^\\) with \\( = 1/2\\) for \\( 1/2\\), \\( = \\) for \\(1/2 < 1\\) and \\(=1\\) for \\( > 1\\). We also analytically characterize the distribution of the diffusive current in the short-time regime using a trajectory-based perturbative approach. Using numerical simulations, we show that in the long-time regime, the diffusive current distribution follows a scaling form with an \\(-\\)dependent scaling function. We also characterise the behaviour of the total current using renewal approach. We find that the average total current also grows algebraically \\( t^\\) where \\( = 1/2\\) for \\( 1\\), \\(=3/2-\\) for \\(1 < 3/2\\), while for \\( > 3/2\\) the average total current reaches a stationary value, which we compute exactly. The variance of the total current also shows an algebraic growth with an exponent \\(=1\\) for \\( 1\\), and \\(=2-\\) for \\(1 < 2\\), whereas it approaches a constant value for \\(>2\\). The total current distribution remains non-stationary for \\(<1\\), while, for \\(>1\\), it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.

How the transport properties of an extended system is affected by coupling to active reservoirs is a significant, yet virtually unexplored question. Here we address this issue in the context of energy transport between two active reservoirs connected by a chain of harmonic oscillators. The couplings to the reservoirs, which exert correlated stochastic forces on the boundary oscillators, lead to fascinating behavior of the energy current and kinetic temperature profile, which we compute exactly in the thermodynamic limit. We show that the stationary active current (i) changes non-monotonically as the activity of the reservoirs are changed, leading to a negative differential conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some finite value of the activity drive. For the example of a dichotomous active force, we find the physical origin of the NDC using nonequilibrium response formalism. It turns out that the kinetic temperature profile remains uniform at the bulk, and can be expressed in a form similar to the thermally driven case. We show that despite this apparent similarity, no effective thermal picture can be consistently built in general. However, such a picture emerges in the small activity limit, where many of the well-known results are recovered.

We investigate the emergent interactions between two active Brownian particles coupled by an attractive harmonic potential and in contact with a thermal reservoir. By analyzing the stationary distribution of their separation, we demonstrate that the effective interaction can be either attractive or repulsive, depending on the interplay between activity, coupling strength, and temperature. Notably, we find that an effective short-range repulsion emerges in the strong and moderate-coupling regimes, when the temperature is below some threshold value, which we characterize analytically. In the strong-coupling regime, the repulsion emerges solely due to the difference in the self-propulsion speeds of the particles. We also compute the short-time position distribution of the centroid of the coupled particles, which shows strongly non-Gaussian fluctuations at low temperatures.