Spectral signature of nonequilibrium conditions

The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time evolution in various ways. Here we review the dynamics of stochastic systems from the viewpoint of nonequilibrium thermodynamics. We explore the effect of external thermodynamic forces on the possible dynamical regimes and show that the time evolution can become intrinsically different under nonequilibrium conditions. For example, nonequilibrium systems with real dynamical components are similar to equilibrium ones when their state space dimension N < 5, but this equivalence is lost in higher dimensions. Out of equilibrium systems thus present new dynamical behaviors with respect to their equilibrium counterpart. We also study the dynamical modes of generalized, non-stochastic evolution operators such as those arising in counting statistics

Bounding the coarse graining error in hidden Markov dynamics

Lumping a Markov process introduces a coarser level of description that is useful in many contexts and applications. The dynamics on the coarse grained states is often approximated by its Markovian component. In this letter we derive finite-time bounds on the error in this approximation. These results hold for non-reversible dynamics and for probabilistic mappings between microscopic and coarse grained states

Nonlinear transport effects in mass separation by effusion

Generalizations of Onsager reciprocity relations are established for the nonlinear response coefficients of ballistic transport in the effusion of gaseous mixtures. These generalizations, which have been established on the basis of the fluctuation theorem for the currents, are here considered for mass separation by effusion. In this kinetic process, the mean values of the currents depend nonlinearly on the affinities or thermodynamic forces controlling the nonequilibrium constraints. These nonlinear transport effects are shown to play an important role in the process of mass separation. In particular, the entropy efficiency turns out to be significantly larger than it would be the case if the currents were supposed to depend linearly on the affinities

Entropy production and time asymmetry in nonequilibrium fluctuations

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant