Related papers: Remarks on Statistical mechanics of a moving syste…
Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles…
For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared…
We resolve the long standing question of temperature dependence of uniformly moving bodies by means of a quantum statistical treatment centred on the zeroth law of thermodynamics. The key to our treatment is the result, established by…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the…
In statistical mechanics the zeroth law of thermodynamics is taken as a postulate which, as its name indicates, logically precedes the first and second laws. Treating it as a postulate has consequences for how temperature is introduced into…
We investigate the emergence of temperature $T$ in the system-plus-reservoir paradigm starting from the fundamental microcanonical scenario at total fixed energy $E$ where, contrary to the canonical approach, $T=T(E)$ is not a control…
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.,…
It is common knowledge that the microcanonical, canonical, and grand-canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive…
We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we…
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…
In a macroscopic (quantum or classical) Hamiltonian system, we prove the second law of thermodynamics in the forms of the minimum work principle and the law of entropy increase, under the assumption that the initial state is described by a…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of 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.…
The canonical ensemble plays a crucial role in statistical mechanics in and out of equilibrium. For example, the standard derivation of the fluctuation theorem relies on the assumption that the initial state of the heat bath is the…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…