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Emergent universal statistics in nonequilibrium systems with dynamical scale selection
Vili Heinonen, Abel J. Abraham, Jonasz Słomka +3
Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal a…
Meaning of temperature in different thermostatistical ensembles
Peter Hänggi, Stefan Hilbert, Jörn Dunkel
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the noti…
Reply to Schneider et al. [arXiv:1407.4127v1]
Jörn Dunkel, Stefan Hilbert
We respond to invalid criticism in the recent Comment by Schneider et al. [arXiv:1407.4127v1]
Thermodynamic laws in isolated systems
Stefan Hilbert, Peter Hänggi, Jörn Dunkel
The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a c…
Reply to Frenkel and Warren [arXiv:1403.4299v1]
Jörn Dunkel, Stefan Hilbert
In their paper [arXiv:1403.4299v1], Frenkel and Warren claim that the Gibbs temperature does not characterize thermal equilibrium correctly. We point out the main logical errors in…
Inconsistent thermostatistics and negative absolute temperatures
Jörn Dunkel, Stefan Hilbert
A considerable body of experimental and theoretical work claims the existence of negative absolute temperatures in spin systems and ultra-cold quantum gases. Here, we clarify that…
Nonlocal observables and lightcone-averaging in relativistic thermodynamics
Jörn Dunkel, Peter Hänggi, Stefan Hilbert
The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables ar…
Stationarity, soft ergodicity, and entropy in relativistic systems
David Cubero, Joern Dunkel
Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the…
Relativistic Brownian Motion
Jörn Dunkel, Peter Hänggi
Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during t…
Time parameters and Lorentz transformations of relativistic stochastic processes
Jörn Dunkel, Peter Hänggi, Stefan Weber
Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized pr…
Thermal equilibrium and statistical thermometers in special relativity
David Cubero, Jesús Casado-Pascual, Jörn Dunkel +2
There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candida…
Relative entropy, Haar measures and relativistic canonical velocity distributions
Jörn Dunkel, Peter Talkner, Peter Hänggi
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting…
Relativistic diffusion processes and random walk models
Jörn Dunkel, Peter Talkner, Peter Hänggi
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability den…
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Jörn Dunkel, Peter Hänggi
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian pa…
Phase Transitions in Small Systems: Microcanonical vs. Canonical Ensembles
Jörn Dunkel, Stefan Hilbert
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) p…
Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation
Stefan Hilbert, Jörn Dunkel
We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interac…
Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
Jörn Dunkel, Peter Hänggi
A theory for (1+3)-dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but…
Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
Jörn Dunkel, Peter Hänggi
We construct a theory for the 1+1-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity, and (ii) reduces to the sta…