Can we make sense of dissipation without causality?

TL;DR

This paper investigates the relationship between dissipation, causality, and stability in relativistic physics, demonstrating that stability is Lorentz-invariant only when causality is preserved, with broad applications across physical theories.

Contribution

It establishes a fundamental link between causality and the Lorentz-invariance of stability in dissipative relativistic systems, supported by multiple physical applications.

Findings

Stability disagreement occurs only if perturbations exit the light-cone.

Dissipative effects can cause observer-dependent stability unless causality is maintained.

14 diverse applications demonstrate the theory's broad relevance.

Abstract

Relativity opens the door to a counter-intuitive fact: a state can be stable to perturbations in one frame of reference, and unstable in another one. For this reason, the job of testing the stability of states that are not Lorentz-invariant can be very cumbersome. We show that two observers can disagree on whether a state is stable or unstable only if the perturbations can exit the light-cone. Furthermore, we show that, if a perturbation exits the light-cone, and its intensity changes with time, due to dissipation, then there are always two observers that disagree on the stability of the state. Hence, ''stability'' is a Lorentz-invariant property of dissipative theories if and only if the principle of causality is respected. We present 14 applications to physical problems from all areas of relativistic physics, ranging from theory to simulation.