Dissipative symmetry breaking in non-equilibrium steady states

Matteo Sireci, Daniel Maria Busiello

Published 2022-12-06Version 1

The connection between dissipation and symmetry breaking is a long-standing enigma in statistical physics. It is intimately connected to the quest of a non-equilibrium functional whose minimization gives the non-equilibrium steady state (NESS). Writing down such a functional, we show that, in the presence of additive noise, any NESS is characterized by the minimum entropy production compatible with the maximum dissipation along cycles in the trajectory space. This result sheds light on the excess entropy production principle and the onset of topological symmetry breaking out-of-equilibrium. Finally, when multiplicative noise is present, we find that the non-equilibrium functional has two dissipative symmetry-breaking contributions, one stemming from cycles and the other from a thermophoresis-like effect. Our framework paves the way to understand selection phenomena as symmetry-breaking processes driven by non-equilibrium dissipation.