Eur. Phys. J. Spec. Top.
https://doi.org/10.1140/epjs/s11734-026-02263-5

Regular Article

Center of mass and equilibrium temperatures of many-identical-particles coupled via bath cross-correlations

¹ Physics Department, Federal University of Paraná, 81531-980, Curitiba, Paraná, Brazil
² Laboratory of Chaomplexity, Interdisciplinary Center for Science, Technology and Innovation (CICTI), Center for Scientific Modeling and Computing (NMCC), Federal University of Paraná, 81531-980, Curitiba, Paraná, Brazil

^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 26 January 2026
Accepted: 6 March 2026
Published online: 24 March 2026

Abstract

This work investigates how correlated environments influence the relative ($T_{\mathrm{eff}}^{(r)}$) and center-of-mass ($T_{\mathrm{eff}}^{(R)}$) effective temperatures using the Langevin description. The procedure is to consider N-identical “independent” particles, each coupled to its own thermal bath at temperature $T_i$ ($i=1,2,\dots ,N$), where correlations among the baths mediate indirectly the coupling between particles. Using Jacobi coordinates, expressions for $T_{\mathrm{eff}}^{(R)}$ and $T_{\mathrm{eff}}^{(r_i)}$ are derived, and it is shown that $T_{\mathrm{eff}}^{(R)}$ can always be identified with the equilibrium temperature obtained from the first law of thermodynamics when N baths are put in thermal contact. The analysis demonstrates that cross correlations between the environments lead to fluctuations effects which are visible in the expression for $T_{\mathrm{eff}}^{(R)}$, highlighting how microscopic noise correlations reshape macroscopic equilibration. Consequently, the procedure allows one to obtain the kind of bath cross-correlations between Langevin equations which correctly mimics the correlations involved in the first law of thermodynamics.