Related papers: Ensemble Inequivalence in Single Molecule Experime…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
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 propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what…
We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the…
Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
We revisit the Rayleigh--Riabouchinsky paradox in dimensional analysis by making explicit the bridge between thermodynamics and the mechanical interpretation of temperature. Boltzmann's constant $k_B$ acts as a dimensional unifier, leading…
The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out…
We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy…
Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several…
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e.,…
A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems…
Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general 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.…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems.…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…