They are expressed in terms of the statistics of fluctuating thermodynamic quantities (heat and work) in a non-equilibrium situation, and are a reflection of an underlying symmetry of the micro-dynamics (typically time-reversal symmetry). Close to equilibrium they imply the well known results of linear response theory (notably the fluctuation dissipation theorem, Kubo relations, Onsager Casimir relations etc), but hold regardless of how far a system is driven away from equilibrium. They can also be understood as a refinement of the second law of thermodynamics. The theory of fluctuation relations has been developed and checked experimentally both for classical and quantum systems, and as well in various non-equilibrium scenarios, namely driven system (closed or open), systems subject to non-equilibrium boundary conditions, or both (heat engines), and even in presence of invasive quantum measurements. I will provide an overview on the subject for the non-specialist.
Collective behavior in biological systems is a complex topic, to say the least. It runs wildly across scales in both space and time, involving taxonomically vastly different organisms, from bacteria and cell clusters, to insect swarms and up to vertebrate groups. It entails concepts as diverse as coordination, emergence, interaction, information, cooperation, decision-making, and synchronization. Amid this jumble, however, we cannot help noting many similarities between collective behavior in biological systems and collective behavior in statistical physics, even though none of these organisms remotely looks like an Ising spin. Such similarities, though somewhat qualitative, are startling, and regard mostly the emergence of global dynamical patterns qualitatively different from individual behavior, and the development of system-level order from local interactions. It is therefore tempting to describe collective behavior in biology within the conceptual framework of statistical physics, in the hope to extend to this new fascinating field at least part of the great predictive power of theoretical physics.
Since the turn of the 20-th century Brownian noise has continuously disclosed a rich variety of phenomena in and around physics. The understanding of this jittering motion of suspended microscopic particles has undoubtedly helped to reinforce and substantiate those pillars on which the basic modern physical theories are resting: Its formal description provided the key to great achievements in statistical mechanics, the foundations of quantum mechanics and also astrophysical phenomena, to name but a few. Recent progress of Brownian motion theory involves (i) the description of relativistic Brownian motion and its impact for relativistic thermodynamics, or (ii) its role for fluctuation theorems and symmetry relations that constitute the pivot of those recent developments for nonequilibrium thermodynamics beyond the linear response.
Although noise commonly is hold as the enemy of order, it in fact also can be of constructive influence. The phenomena of Stochastic Resonance and Brownian motors present two such archetypes wherein random Brownian dynamics together with unbiased nonequilibrium forces beneficially cooperate in enhancing detection and/or in facilitating directed transmission of information. The applications range from information processing devices in physics, chemistry, and physical biology to new hardware for medical rehabilitation. Particularly, additional non-equilibrium disturbances enable the rectification of haphazard Brownian noise so that quantum and classical objects can be directed along on a priori designed routes (i.e. Brownian motors). We conclude with an outlook of future prospects, trends and unsolved issues.