Related papers: Alternative Derivation of the Partition Function f…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is environments described by the Generalized or Gibbs canonical ensemble. We demonstrate…
We study the Hamiltonian Mean Field (HMF) model, a system of $N$ fully coupled particles, in the microcanonical ensemble. We use the previously obtained free energy in the canonical ensemble to derive entropy as a function of energy, using…
We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as $S_d=-\sum_n \rho_{nn}\ln \rho_{nn}$ with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the…
It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics…
In this chapter we address the topic of quantum thermodynamics in the presence of additional observables beyond the energy of the system. In particular we discuss the special role that the generalized Gibbs ensemble plays in this theory,…
A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and…
Starting from the quantum mechanics for $N$ particles, we show that we can directly derive the microcanonical ensemble average of the physical quantity $A$ by using only the long time average and the equal probability assumption for the…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…
This article is a short version of a longer article to appear in Physics Reports (cond-mat/9708200). The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of…
We consider a small Hamiltonian system strongly interacting with a much larger Hamiltonian system (the bath), while being driven by both a time-dependent control parameter and non-conservative forces. The joint system is assumed to be…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…
Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to…
Based on the properties of exponential distribution families we analyze the Fisher information of the Gibbs canonical ensemble to construct a new state function for simple systems with no mechanical work. Such a function possesses nice…
Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…