Microlagrangian manifolds and quasithermodynamic fluctuations of nonequilibrium states

TL;DR

This paper introduces a novel quantization framework for nonequilibrium thermodynamics using quasithermodynamic fluctuations, leading to new equations, inequalities, and interpretations analogous to quantum mechanics.

Contribution

It develops a semiclassical quantization approach for thermodynamic manifolds, introducing thermocorpuscles and deriving new fluctuation equations and inequalities.

Findings

Derivation of quasithermodynamic fluctuation equations

Proposal of a thermodynamic Bell's inequality and its potential violation

Interpretation of a nonequilibrium partition function as an expectation of second quantized operators

Abstract

The paper deals with "quantization" and "second quantization" of phenomenological thermodynamics with respect to the Boltzmann's constant. It is suggested to perceive the quasithermodynamic parameter (corresponding to the Boltzmann's constant) as a mathematical analogue of the semiclassical parameter (corresponding to the Planck's constant), and to introduce a new concept of a "thermocorpuscle" (a thermodynamic analogue of a particle where the coordinates are replaced by the nonequilibrium thermodynamic forces and the momenta are replaced by the corresponding flows). The semiclassical quantization of phenomenological thermodynamic Lagrangian manifolds yields a new system of equations for the quasithermodynamic fluctuations along a curve of evolution of a nonequilibrium physical system. This leads to a quasithermodynamic analogue of Bell's inequalities and their violation is a new effect that can be tested experimentally. The generating function of the quasithermodynamic fluctuations (the nonequilibrium analogue of a partition function) is interpreted as an expectation value of a second quantized operator expressed via the density of thermocorpuscles. An analogue of the BBGKY chain of equations defines a deformation of the fluctuations by an interaction between the thermocorpuscles. In place of an interaction parameter in mechanics (the "external" Planck's constant), one introduces the "external" Boltzmann's constant for an asymptotic expansion of the thermodynamic collision integral.