A specification of the maxwell-rayleigh-heisenberg approach to modelling fluids for bioelectronic applications

The key question which any version of random fluid mechanics has to resolve is how to provide continuous probability distributions for the fluid particles. Each specific way is determined by one or another set of assumptions. Statistical mechanics proceeds on the thermodynamic-limit assumption supposing that the domain occupied by the fluid is "macroscopically big" and the number of the particles in it is "statistically large". This picture cannot be the case in mesoscopic systems. The latter are common in many modern applications including bioelectronics. The present work develops a nonstatistical way to provide the above continuous distributions. It follows the vision formed by certain results of Heisenberg, Rayleigh, and Maxwell and specifies it by means of extending nonlinear nonequilibrium stochastic hydrodynamics (NNSHD) introduced by the authors earlier. The work concentrates on the following two generalizations: first, allowing for nonzero volumes of the particles, the feature typical in the biological parts of bioelectronic problems, and, second, accounting the general kinetic-energy/momentum dependences, including the relativistic ones, which are usually necessary in the electronic parts of bioelectronic problems. The simplest case of the first generalization is exemplified with an evaluation of the electrochemical potentials and pressures of red blood cells in human blood in a recently published paper of the authors. The second generalization is illustrated in Section 10 of the present work with the relativistic distribution functions which take into account the general spin picture of composite particles by means of the model of composons, the flexible combination of bosons and fermions based on the generalized-kinetics (GK) methods. The above generalization is intended to be a framework rather than theory that inherently includes the capabilities in coupling to other fluid-modelling treatments like common hydrodynamics or stochastic kinetic equations. The issues on further extensions in line with GK and on the coupling to the latter are emphasized. A few directions for future research are discussed as well.