Modified Wave Equation: Wave Equation for Non-Equilibrium Systems

Abstract

The wave equations takes into account only the motion of the particle in n-dimensions and at a time t. This can also be called a space-time metric. For example in topology, let χ be a set. Let the collection of all the subsets of χ be τ. So, the topological space may be considered as (χ,τ) iff: ∅∈τ χ∈τ If A∈τ⋀B∈τ, then A∪B∧A∩B∈τ0. Where the basis is defined by U∈τ∧p∈U,∃V∈B such that p∈V⊂B And sub-basis by For U∈τ,p∈U,∃〈V_i 〉∈B such that p∈ ⋂_(i=1)^n V_i ⊂B Here the metric chosen is (C,g), where g is the metric tensor. Here, g characterizes the system’s surface area, volume, position in n-dimensions. But the general wave equation doesn’t consider the change of surface area of the system with respect to time. This is for non-equilibrium systems. The system is unstable. So, considering the change of surface area and volume along with the n- dimensional position change, the wave equation for the non-equilibrium unstable systems can be described. A system is said to be in non-equilibrium if the internal parameters of the system is constantly in change and hence the system is unstable.