Heat fluctuations in the logarithm-harmonic potential

Thermodynamic quantities, like heat, entropy, or work, are random variables, in stochastic systems. Here, we investigate the statistics of heat exchanged by a Brownian particle subjected to logarithm-harmonic potential. We derive analytically characteristic function and its moments for heat. Through numerical integration, simulation, calculate probability distribution as well, characterizing fully statistical behavior The results also investigated asymptotic limit, where encounter terms hypergeometric functions.