Related papers: Data processing theorems and the second law of the…

$H$-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of…

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function…

The classical thermodynamic laws fail to capture the behavior of systems with energy Hamiltonian which is an explicit function of the temperature. Such Hamiltonian arises, for example, in modeling information processing systems, like…

We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the…

We derive a generalization of the Second Law of Thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be…

Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…

We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynamics, for situations involving information processing. To this end, we consider an information reservoir (representing, e.g. a…

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…

We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when…

We provide a simple physical interpretation, in the context of the second law of thermodynamics, to the information inequality (a.k.a. the Gibbs' inequality, which is also equivalent to the log-sum inequality), asserting that the relative…

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…

In this paper we discuss about the validity of the Shannon entropy functional in connection with the correct Gibbs-Hertz probability distribution function. We show that there is no contradiction in using the Shannon-Gibbs functional and…

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…

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 this paper, we derive a generalized second fluctuation-dissipation theorem (FDT) for stochastic dynamical systems in the steady state. The established theory is built upon the Mori-type generalized Langevin equation for stochastic…

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…

Extending the quantum formulation of [Phys. Rev. X 3, 041003 (2013)] to a more general setting for studying the thermodynamics of information processing including initial correlations, we generalize the second law of thermodynamics to…

Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…

In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results…