Entropy Currents for Reversible Processes in a System of Differential equations. -- The Case of Latticized Classical Field Theory --

TL;DR

This paper explores the concept of entropy currents in a complex lattice field theory system, demonstrating multiple conserved entropy currents under reversible, adiabatic conditions in a two-dimensional case.

Contribution

It introduces a framework for defining multiple entropy currents in lattice field theories, extending thermodynamic concepts to complex differential equation systems.

Findings

Multiple entropy currents can be defined in lattice field theories.

All entropy currents are conserved under adiabatic, reversible conditions.

Three distinct entropy currents are identified in a 2D lattice field theory example.

Abstract

We consider a very complicated system of some latticized differential equations that is considered as equations of motion for a field theory. We define macro state restrictions for such a system analogous to thermodynamical states of a system in statistical mechanics. For the case in which we have assumed adiabaticity in a generalized way which is equivalent to reversible processes. It is shown that we can define various entropy currents, not only one. It is indeed surprising that, for a two dimensional example of lattice field theory, we get three different entropy currents, all conserved under the adiabaticity condition.