相关论文: Boltzmann conjecture, meta-equilibrium entropy, se…
Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis,…
The physical meaning of entropy is analyzed in the context of statistical, nuclear, atomic physics and cosmology. Only the microcanonical Boltzmann entropy leads to no contradictions in several simple, elementary and for thermodynamics…
All of the basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system…
The dynamical justifications which lie at the basis of an effective Statistical Mechanics for self gravitating systems are formulated, analyzing some among the well known obstacles thought to prevent a rigorous Statistical treatment. It is…
This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by…
I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that…
The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each…
Are your perceptions, memories and observational data, a statistical fluctuation out of the thermal equilibrium of the universe, having no correlation with the actual past state of the universe? Arguments are given in the literature for and…
Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation - now called the Boltzmann…
Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical…
Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of…
We prove the eventological $H$-theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of…
Boltzmann's principle S=k ln W allows to extend equilibrium thermo-statistics to ``Small'' systems without invoking the thermodynamic limit. The clue is to base statistical probability on ensemble averaging and not on time averaging. It is…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
The critique against using Boltzmann's microcanonical entropy, an "ensemble measure", as foundation of statistics is rebuffed. The confusion of the microcanonical distribution with the exponential Boltzmann-Gibbs (``BG'') distribution is…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…