Related papers: Smoothness of Wave Functions in Thermal Equilibriu…
The recent remarkable developments in quantum optics, mesoscopic and cold atom physics have given reality to wave functions. It is then interesting to explore the consequences of assuming ensembles over the wave functions simply related to…
The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the…
For classical systems, expectation value of macroscopic property in equilibrium state can be typically provided through thermodynamic (so-called canonical) average, where summation is taken over possible states in phase space (or in…
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…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We focus attention upon the thermal statistics of the classical analogs of quasi-probabilities's (QP) in phase space for the important case of quadratic Hamiltonians. We consider the three more important OPs: 1) Wigner's, $P$-, and…
Involvement of the environment is indispensable for establishing the statistical distribution of system. We analyze the statistical distribution of a quantum system coupled strongly with a heat bath. This distribution is determined by…
Superstatistics (Physica A 322, 267-275, 2003) is a formalism that attempts to explain the presence of distributions other than the Boltzmann-Gibbs distributions in Nature, typically power-law behavior, for systems out of equilibrium such…
This paper is about nonequilibrium steady states (NESS) of a class of stochastic models in which particles exchange energy with their "local environments" rather than directly with one another. The physical domain of the system can be a…
We consider an isolated, macroscopic quantum system. Let H be a micro-canonical "energy shell," i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + delta E. The…
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…
We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi, Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable model of an…
Thermalization is the process through which a physical system evolves toward a state of thermal equilibrium. Determining whether or not a physical system will thermalize from an initial state has been a key question in condensed matter…
This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very…
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…
When a physical system is put in contact with a very large thermal bath, it undergoes a dissipative (i.e., an apparently irreversible) process that leads to thermal equilibrium. This dynamical process can be described fully within quantum…
The partition function of a bosonic Riemann gas is given by the Riemann zeta function. We assume that the hamiltonian of this gas at a given temperature $\beta^{-1}$ has a random variable $\omega$ with a given probability distribution over…
We provide here an explicit example of Khinchin's idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical…
Departures of observables from their thermal equilibrium expectation values are studied under heat flow in steady-state non-equilibrium environments. The relation between the spatial and temperature dependence of these non-equilibrium…
Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states.…