Related papers: Boltzmann-Kolmogorov equation
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…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
In this work, we consider a 2-state quantum system interacting with a thermal reservoir. By computing the long time limit of the probability for the system to be in the ground state according to the Schrodinger/Von Neumann equation, we…
We consider the system of particles on a finite interval with pair-wise nearest neighbours interaction and external force. This model was introduced by Malyshev to study the flow of charged particles on a rigorous mathematical level. It is…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state are considered. While for stationary states with a constant kinetic energy the two rates…
Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ specifies the…
This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain H\"older-type classes in which a random field is…
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…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
This contribution is dedicated to dilucidating the role of the Gibbs entropy in the discussion of the emergence of irreversibility in the macroscopic world from the microscopic level. By using an extension of the Onsager theory to the phase…