Niet-evenwicht bij lage temperatuur

Summary The theory of nonequilibrium is not a completed edifice. Yet most processes occurring in nature happen far from equilibrium, with life itself as a rather relevant example. This thesis attempts to contribute to our understanding of non-equilibrium processes. The work can be divided into three parts: First, we give a low-temperature formula for the stationary occupations in Markovian systems away from detailed balance. Three applications are discussed, one to determine the direction of the ratchet current, one to population inversion, and finally, we determine the low-temperature behavior of a one-dimensional diffusive lattice gas subject to exclusion and with nearest neighbor interaction. The first and second can take advantage of low temperature to improve the gain and typical nonequilibrium features. The new formula brings to the foreground the importance of kinetic (i.e. non-thermodynamical) aspects of low-temperature analysis. The work discussed here was reported before in [1], [2]. Secondly, we extend the low-temperature framework to include some dynamical aspects. It should come as no surprise that the path-probability function plays a central role when studying dynamics. For example, we could be interested in the heat produced by a system up to time $t$. The average heat is a weighted sum over trajectories of the accumulated heat up to time $t$. An important feature of the type of dynamics we consider is that it may exhibit many well-separated time scales. States frozen on a certain time scale typically open their escape channels only when time becomes large enough at low temperatures, provided the time scale is allowed to scale exponentially. The first result of this part is a low-temperature formula for the path-probability function of a Markov jump process. The second result is that we show that the recently proposed non-equilibrium heat capacity vanishes in the zero-temperature limit for systems exhibiting a single low-temperature state. Some part of the discussion is currently in preparation [3], [4]. Thirdly, we study the kinetic aspect of stochastic transport in two-headed molecular motor proteins such as Myosin V, Dynein or Kinesin. Such systems are sometimes modeled as ratchets, yet we claim they are not, at least not with a flashing asymmetric potential; the crucial asymmetry is in the dynamical activity. We make this explicit in terms of a simple Markov model, emphasizing the kinetic (and non-thermodynamic) aspects of stochastic transport. The analysis shows the presence of a fluctuation symmetry in that part of the dynamical activity which is antisymmetric under reversal of the two heads of the motor. The direction of the motor motion is determined by it. The work discussed in this part was reported before in [5]. References [1] C. Maes and W. O'Kelly de Galway. A Low Temperature Analysis of the Boundary Driven Kawasaki Process, J. Stat. Phys., 153:991-–1007, 2013. [2] C. Maes, K. Netočný and W. O'Kelly de Galway. Low temperature behavior of nonequilibrium multilevel systems, J. Phys. A, 47(3):035002, 2014. [3] K. Netočný and W. O’Kelly de Galway, Noneqilibrium heat capacities at low temperatures, in preparation. [4] K. Netočný and W. O’Kelly de Galway, Nonequilibria at low temperatures, in preparation. [5] C. Maes and W. O’Kelly de Galway, On the kinetics that moves molecular motors, Physica A: Statistical Mechanics and its Applications, 436:678-685, 2015.nrpages: 150status: publishe