Galilean invariance is a cornerstone of classical mechanics. It states that the equations of motion are the same in different inertial frames meaning they do not change under a Galilean transformation. Inertial frames, in turn, are reference frames describing closed systems where the frame-internal physics is not affected by frame-external forces. The description of real world systems,...

The generalized Cattaneo equation (GTE) involving memory effect is introduced by smearing the time derivatives. Consistency conditions which the smearing functions obey restrict freedom in their choice. The proposed scheme goes beyond the approach based on using fractional derivatives. I present the conditions under which solutions of the GTE can be recognized as probability distribution, i.e....

The optimal fluctuation method — essentially geometrical optics — gives a valuable insight into large deviations of constrained Brownian motion, and it achieves this purpose by simple means. I will illustrate these points by revisiting the Airy distribution - the probability distribution of the

area under a Brownian excursion - and considering some additional statistics of Brownian...

We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the time-averaged velocity of the piston in the long-time limit, we perturbatively calculate the large deviation function of the time-averaged velocity. Then, we...

We study simple random-walk models with asymmetric time delays. Probability of a walker to move to the right or to the left depends on a difference between two state-dependent functions evaluated at states of the walker at two different times in the past. This might be seen as a model of a discrete replicator dynamics with strategy-dependent time delays. We assume hyperbolic-tangent fitness...