Thermostatistics of a damped bi-modal particle

Resumo

We study the thermostatistics of a damped bi-modal particle, i.e., a particle of mass m
subject to a work reservoir that is analytically represented by the telegraph noise. Because of
the coloured nature of the noise, this system does not t the Levy-It^o class of stochastic processes
making of it an instance of a non-equilibrium system in contact with an external reservoir. We
obtain the statistics for the position and velocity, namely in the steady state, as well as the (time
dependent) statistics of the energy  uxes in the system considering no constraints on the noise
features. With that results we are able to give an account of the statistical features of the large
deviations of the injected and dissipated power that can change from sub-Gaussianity to super-
Gaussianity depending on the colour of the noise. By properly dening an effective temperature
for this system, T , we are capable of obtaining an equivalent entropy production/exchange rate
equal to the ratio between the dissipation of the medium,  and the mass the particle, a relation
that concurs with the case of a standard thermal reservoir at temperature, T = T .