Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields

Abstract

Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An outstanding challenge is the thermodynamically consistent formulation of the underlying stochastic dynamics that obeys local detailed balance and allows for a rigorous analysis of the stochastic thermodynamics of non-reciprocally interacting particles. Here, we present such a framework for a broad class of active systems and derive by systematic coarse-graining exact expressions for the macroscopic entropy production. Four independent contributions to the thermodynamic dissipation can be identified, among which the energy flux sustaining vorticity currents manifests the presence of non-reciprocal interactions. Then, Onsager's non-reciprocal relations, the fluctuation-response relation, the fluctuation relation and the thermodynamic uncertainty relations for non-reciprocal systems are derived. Finally, we demonstrate that our general framework is applicable to a plethora of active matter systems and chemical reaction networks and opens new paths to understand the stochastic thermodynamics of non-reciprocally interacting many-body systems.

Figures (2)

• Figure 1: Scheme of various levels of coarse-graining considered in this paper, microscopic, mesoscopic, macroscopic-fluctuating, macroscopic-deterministic and hydrodynamic. (a) Microscopic particles are confined to the lattice site (denoted by the black $\#$). Four different types of particles are illustrated: triangle (blue), square (pink), pentagon (green) and, circle (orange). (b/c) The mesoscopic/macroscopic description is obtained for the fluctuating particle number/density. (d) The straight interface between the density fields represents the suppression of the fluctuation and convergence to the mean-field dynamical description. (e) Cyan and Yellow denote the relevant hydrodynamic order parameter that does not necessarily preserve the microscopic properties.
• Figure 2: (a) Illustration of the microscopic interactions between particle types, denoted by $v_{ij}$, confined to the lattice site $\#$, with $v_{ij} \neq v_{ji}$. (b) All possible transitions are indicated by curved harpoons. The exact expressions for two transition rates $k_{\gamma\gamma'}$ in terms of $v_{ij}$ for the microscopic lattice configuration in \ref{['fig:CG_diagram']}(a) are demonstrated.