相关论文: In Search of H-theorem for Ulam's Redistribution P…

We discuss a possibility of deriving an H-theorem for nonlinear discrete time evolution equation that describes random wealth exchanges. In such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a…

H-theorem gives necessary conditions for a system to evolve in time with a non-diminishing entropy. In a quantum case the role of H-theorem plays the unitality criteria of a quantum channel transformation describing the evolution of the…

The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian dynamics for…

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We…

In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential…

A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of…

We discuss a nonlinear model for the relaxation by energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels e_i with i=1,2,...,N. The time-dependent occupation probabilities…

In the present effort we consider the most general non linear particle kinetics within the framework of the Fokker-Planck picture. We show that the kinetics imposes the form of the generalized entropy and subsequently we demonstrate the…

In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.

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…

The $H$-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium.…

We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive {\it master equations} for the dynamics of the expected power in the discrete modes. In…

The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…

Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…

The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…

In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we…

An extension of the H-theorem for dissipative particle dynamics (DPD) to the case of a multi-component fluid is made. Detailed balance and an additional H-theorem are proved for an energy-conserving version of the DPD algorithm. The…

A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…

Boltzmann's H-function H(t) holds a venerable place in the history of science. However, it seems never to have been evaluated for particles with orientational degrees of freedom. We generalize Boltzmann's H-function to a gas of molecules…