Center of mass and equilibrium temperatures of many-identical-particles coupled via bath cross-correlations
Year: 2026
Type: article
Abstract: This work investigates how correlated environments influence the relative ( $$T_{\mathrm{eff}}^{(r)}$$ T eff ( r ) ) and center-of-mass ( $$T_{\mathrm{eff}}^{(R)}$$ T 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 $$T_i$$ T i ( $$i=1,2,\ldots ,N$$ i = 1 , 2 , … , N ), where correlations among the baths mediate indirectly the coupling between particles. Using Jacobi coordinates, expressions for $$T_{\mathrm{eff}}^{(R)}$$ T eff ( R ) and $$T_{\mathrm{eff}}^{(r_i)}$$ T eff ( r i ) are derived, and it is shown that $$T_{\mathrm{eff}}^{(R)}$$ T 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 $$T_{\mathrm{eff}}^{(R)}$$ T 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.
Institution: Universidade Federal do Paraná
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
Awards: G3690646728, G4105071713, G5372751196
OpenAlex ID: W7140199470