Biomedical subjects
Publications and source records attributed to A R Plastino.
We show that the invariance of entropic distances under Liouville dynamics yields classical analogues of information-related, quantum mechanical impossible operations. By recourse to Fisher's information measure, we also establish a connection between such classically forbidden operations and statistical estimation theory.
As recently shown, a constrained Fisher-information extremizing (CFIE) process is able to deal with both equilibrium and nonequilibrium thermodynamic processes, thus being able to reproduce results deduced by a recourse to Boltzmann's transport equation (BTE). Here, we discuss the propagation of sound waves in a dilute gas and compare the ensuing CFIE solutions with those obtained by a recourse to Grad's approach to the BTE. The final molecular distribution function arrived at is the same following two alternative routes, either (i) the BTE via the Grad approach or (ii) the constrained Fisher treatment that does not require the use of the BTE. The way the necessary a priori information is used in these two instances, is however, quite different.
It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both nonequilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground-state solution, and nonequilibrium thermodynamics corresponds to excited-state solutions, of a Schrödinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium and nonequilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis. As an application, we discuss viscosity in dilute gases.
A classical version of the no-cloning theorem is discussed. We show that an arbitrary probability distribution associated with a (source) system cannot be copied onto another (target) system while leaving the original distribution of the source system unperturbed. For classical dynamical systems such a perfect cloning process is not permitted by the Liouvillian (ensemble) evolution associated with the joint probability distribution of the composite source-target-copying machine system.
The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis." For q>0, the q-transport equation satisfies an H theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.
It is shown that the Legendre-transform structure of thermodynamics can be replicated without any change if one replaces the entropy S by Fisher's information measure I. Also, the important thermodynamic property of concavity is shown to be obeyed by I. By this use of the Fisher information measure we develop a thermodynamics that seems to be able to treat equilibrium and nonequilibrium situations in a manner entirely similar to the conventional one.