相关论文: The coefficient of restitution does not exceed uni…
We consider overdamped Brownian particles with two degrees of freedom (DoF) that are confined in a time-varying quadratic potential and are in simultaneous contact with heat baths of different temperatures along the respective DoF. The…
Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines by bounding the maximal amount of mechanical energy produced compared to the amount of heat required. While this was accomplished early on, by Carnot and…
We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a…
The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated…
Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they often do not respect the laws of…
The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions to the Boltzmann…
We study the nonrelativistic limit of the motion of a classical particle in a model of deformed special relativity and of the corresponding generalized Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic classical…
The field-dependent equilibrium thermodynamics is derived with two methods: either by using the potential formalism either by the statistical method. Therefore, Pontrjagin's extremum principle of control theory is applied to an extended…
A superfluid in the absence of the viscous normal component should be the best realization of an ideal inviscid Euler fluid. As expressed by d'Alembert's famous paradox, an ideal fluid does not exert drag on bodies past which it flows, or…
We provide a quantum statistical thermodynamical solution of the long standing problem of temperature transformations of uniformly moving bodies. Our treatment of this question is based on the well established quantum statistical result…
To prove by probabilistic methods that every $(n-1)$-dimensional section of the unit cube in $R^n$ has volume at most $\sqrt 2$, K. Ball made essential use of the inequality $$ \frac{1}{\pi}\int_{-\infty}^{\infty} \left(\frac{\sin^2…
According to classical Boltzmannian thermodynamics, the efficiency of a cyclic machine is strictly lower than one. Such a result is a straightforward consequence of the second principle of thermodynamics. Recent advances in the study of the…
When the energy content of a resonant mode of a crystalline solid in thermodynamic equilibrium is directly measured, assuming that quantum effects can be neglected it coincides with temperature except for a proportionality factor. This is…
Spin-echo experiments are often said to constitute an instant of anti-thermodynamic behavior in a concrete physical system that violates the second law of thermodynamics. We argue that a proper thermodynamic treatment of the effect should…
A geometric foundation thermo-statistics is presented with the only axiomatic assumption of Boltzmann's principle S(E,N,V)=k\ln W. This relates the entropy to the geometric area e^{S(E,N,V)/k} of the manifold of constant energy in the…
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…
The integral law of thermal radiation by finite size emitters is studied. Two geometrical characteristics of a radiating body or a cavity, its volume and its boundary area, define two terms in its radiance. The term defined by the volume…
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…
A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the…
The question of Bohr correspondence in quantum field theory is considered from a dynamical point of view. It is shown that the classical description of particle interactions is inapplicable even in the limit of large particles' masses…