Related papers: Boltzmann's Approach to Statistical Mechanics
The second law of thermodynamics is asymmetric with respect to time as it says that the entropy of the universe must have been lower in the past and will be higher in the future. How this time-asymmetric law arises from the time-symmetric…
In a recent perspective article, Horowitz and Gingrich discuss thermodynamic uncertainty relations that have been derived using "stochastic thermodynamics", a theory based on a hypothesis known as local detailed balance. The authors…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this…
The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it.…
Recently, there has been a considerable progress on the issue of the thermodynamic second law, which is known as the law of entropy increase or irreversibility. In particular, a novel symmetry known as the Gallavotti-Cohen symmetry is found…
In this report we discuss the organization of different levels of nature and the corresponding space-time structures by the consideration of a particular problem of time irreversibility. The fundamental time irreversibility problem consists…
There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this…
The Boltzmann distribution (the most probable distribution) is one of the most important concepts used in physics, chemistry and biology. Suppose we put the system initially in one of the less probable state then the system will find 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…
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 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…
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 will be shown, how the Boltzmannian ideas on statistical physics can be naturally applied to nonequilibrium thermodynamics. A similar approach for treating nonequilibrium phenomena has been successfully used by Einstein and Smoluchowski…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
We proved when random-variable fluctuations obey the central limit theorem the equality of the uncertainty relation corresponds to the thermodynamic equilibrium state. The inequality corresponds to the thermodynamic non-equilibrium state.…
The possible distinction between inanimate and living matter has been of interest to humanity since thousands of years. Clearly, such a rich question can not be answered in a single manner, and a plethora of approaches naturally do exist.…
It is proved in the paper that the non-conservative dissipative force and asymmetry of time reversal can be naturally introduced into classical statistical mechanics after retarded electromagnetic interaction between charged microparticles…
The second law of thermodynamics states that the entropy of an isolated system can only increase over time. This appears to conflict with the reversible evolution of isolated quantum systems under the Schr\"odinger equation, which preserves…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…