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A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
We use computer simulations to study the microscopic dynamics of an athermal assembly of soft particles near the fluid-to-solid, jamming transition. Borrowing tools developed to study dynamic heterogeneity near glass transitions, we…
We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
Systems driven far from equilibrium may exhibit anomalous density fluctuations: active matter with orientational order display giant density fluctuations at large scale, while systems of interacting particles close to an absorbing phase…
A system of a metastable phase with several sorts of the heterogeneous centers is considered. An analytical theory for the process of condensation in such a system is constructed in dynamic conditions. The free energy of formation of the…
We study properties of steady states (states with time-independent density operators) of systems of coupled harmonic oscillators. Formulas are derived showing how adiabatic change of the Hamiltonian transforms one steady state into another.…
For two-dimensional many-particle systems first-order, second-order, single step continuous, as well as two-step continuous (KTHNY-like) melting transitions have been found in previous studies. Recent computer simulations, using particle…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in…
By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair…
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…
Multistability is an inseparable feature of many physical, chemical and biological systems which are driven far from equilibrium. In these nonequilibrium systems, stochastic dynamics often induces switching between distinct states on…
We reveal several distinct regimes of the relaxation dynamics of a small quantum system coupled to an environment within the plane of the dissipation strength and the reservoir temperature. This is achieved by discriminating between…
Nanoparticles levitated in an optical trap provide a versatile platform to study mechanical oscillators in a controlled environment with tuneable parameters. Recently, it has become possible to couple two of these optomechanical…
Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…