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Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…
The optimization of the conversion of thermal energy into work and the minimization of dissipation for nano- and mesoscopic systems is a complex challenge because of the important role fluctuations play on the dynamics of small systems. We…
The steady state heat currents of continuous absorption machines can be decomposed into thermodynamically consistent contributions, each of them associated with a circuit in the graph representing the master equation of the thermal device.…
We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this…
Periodic driving of quantum dots is analyzed as a basis for developing dynamic switching devices. We study transport through periodically modulated energy levels which are coupled to leads via tunneling coefficients. Utilizing Floquet…
We show that the fraction of time a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by L\'evy for Brownian motion. Stochastic currents with long streaks above or below their average…
We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the micro canonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a…
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely unexplored theoretically due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum…
In the realm of statistical mechanics, it has been established that there is no distinction between the micro-canonical and canonical ensembles in the thermodynamic limit. However, this paradigm may alter when addressing statistical…
We present a detailed description of semi-quantum molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian…
We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density dependent chemical potentials. From the corresponding Onsager relations we extract linear…
We study the classical statistical mechanics of a phase-space curve. This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom.…
We derive explicit forms of Markovian transition probability densities for the velocity space, phase-space and the Smoluchowski configuration-space Brownian motion of a charged particle in a constant magnetic field. By invoking a…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
We formulate a full-counting statistics description to study energy exchange in multi-terminal junctions. Our approach applies to quantum systems that are coupled either additively or non-additively (cooperatively) to multiple reservoirs.…
The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat - the Gallavotti-Cohen Theorem -- relies on the ergodic properties of the system considered. We show that when perturbed by an…