Related papers: Data processing theorems and the second law of the…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
We present a general framework for systems which are prepared in a non-stationary non-equilibrium state in the absence of any perturbation, and which are then further driven through the application of a time-dependent perturbation. We…
The Hahn-Banach Theorem, a cornerstone of modern functional analysis, is a natural companion of the Second Law of Thermodynamics. From a Kelvin-Planck version of the Second Law, the Hahn-Banach Theorem delivers, immediately and…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…
With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistic physics.…
We test Boltzmann's H-theorem for several models of particle random walk. We study the influence of interaction between the particle and reservoir/detectors on entropy and find entropy increasing in time for some models and behaving…
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…
We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer's principle (namely, that erasure of information produces at least the equivalent…
Complex systems that are characterized by strong correlations and fat-tailed distribution functions have been argued to be incompatible within the framework of Boltzmann-Gibbs entropy. As an alternative, so-called generalized entropies were…
We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single…
We provide a stochastic mathematical representation for Clausius' and Kelvin-Planck's statements of the Second Law of Thermodynamics in terms of the entropy productions of a finite, compact driven Markov system and its lift. A surjective…
A unification of thermodynamics and information theory is proposed. It is argued that similarly to the randomness due to collisions in thermal systems, the quenched randomness that exists in data files in informatics systems contributes to…
Boltzmann's principle S(E,N,V)=k\ln W relates the entropy to the geometric area e^{S(E,N,V)} of the manifold of constant energy in the N-body phase space. From the principle all thermodynamics and especially all phenomena of phase…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic…
Hunt's hypothesis (H) and the related Getoor's conjecture is one of the most important problems in the basic theory of Markov processes. In this paper, we investigate the invariance of Hunt's hypothesis (H) for Markov processes under two…
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…
So far, feedback-driven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system or (iii) by identifying an implicit Maxwell demon in steady state transport. We derive the corresponding second…
The laws of thermodynamics, despite their wide range of applicability, are known to break down when systems are correlated with their environments. Here, we generalize thermodynamics to physical scenarios which allow presence of…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…