The heat distribution in a logarithm potential

Abstract

All statistical information about heat can be obtained with the probability distribution of the heat functional. This paper derives analytically the expression for the distribution of the heat, through path integral, for a diffusive system in a logarithm potential. We apply the found distribution to the first passage problem and find unexpected results for the reversibility of the distribution, giving a fluctuation theorem under specific conditions of the strength parameters.

Heat has a kinetic term in overdamped stochastic thermodynamics

“…Here we show the modification of another interesting case of the heat distribution in the logarithm potential calculated without correction by one of the authors in [15]. The logarithm potential appears in different stochastic phenomena [24][25][26][27][28][29][30].…”

“…where now k is the strength of the logarithm potential and now x(t) is defined only in the positive real axis [31], and now the initial distribution of the position is a Dirac delta [15]. Now we will explicitly show the modifications that one have to consider when calculate the heat distribution.…”

“…If we define Q = Q − ∆K, the calculation can be carried along the same lines in reference [15]. However we will still need to integrate the velocities.…”

“…Namely, quantities like heat and work now become fluctuating quantities. A lot of attention was devoted to obtaining the probability distribution for these thermodynamic functionals, with experimental [7][8][9][10] and theoretical [11][12][13][14][15][16][17] calculations. This microscale thermodynamics is now a proper field of research, that is now called stochastic thermodynamics [18][19][20].…”

Stochastic Thermodynamics of a Piezoelectric Energy Harvester Model

“…Very recently, thermodynamic uncertainty relations bounding the signal to noise ratio of a measured current have been also discovered [15]. In particular, the study of work and heat fluctuations has been the object of focus in several systems, such as overdamped linear Langevin Equation [16], particle diffusion in time-dependent potentials [17][18][19][20][21][22], Brownian particles driven by correlated forces [23], general thermal systems [24], asymmetric processes [25], underdamped Langevin Equation [26], or in transient relaxation dynamics [27]. The interest in these quantities is motivated by the search for optimization protocols in models of stochastic engines or, from a more theoretical perspective, by the general symmetry properties or by singular behaviors that work and heat distributions can show [28].…”