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Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states…
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way,…
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In…
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems…
All the laws of physics are time-reversible. Time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the entropy and the second law of thermodynamics are introduced. In…
Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time-reversibility have so far been limited to microscopic models.…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
We present a relativistic quantum mechanics of a point mass with absolute thermodynamic time and temperature, combined to a single complex parameter of evolution. In this theory, the geometric time is introduced as one of space-time…
The second law of thermodynamics - the usual statement of the arrow of time - has been called the most fundamental law of physics. It is thus difficult to conceive that a single dynamical system could contain subsystems, in significant…
We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and…
An attempt is made to de-mystify the apparent "paradox" between microscopic time revsersibility and macroscopic time irreversibility. It is our common experience that a hot cup of coffee cools down to room temperature and it never…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
A non-local toy-model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase. It is…
In calorimetry and particularly in heat capacity measurements, different characteristic relaxation time constants may perturb the experiment which cannot be considered at thermodynamic equilibrium. In this case, thermodynamics of…
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at…
We consider thermal relaxation process of a quantum system attached to a single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is…
We analyze underdamped Brownian motion in non-isothermal media with quadratic, linear, and piecewise-constant temperature profiles. Exact identities for entropy production and entropy extraction are derived, addressing whether a vanishing…
We establish an algebraic criterion which ensures the strict positivity of the entropy production in quantum models consisting of a small system coupled to thermal reservoirs at different temperatures.
We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen…
The approach to the analysis of the dynamic of non-equilibrium open systems within the framework of the laws of classical mechanics on the example a hard-disks is offered. This approach was based on Hamilton and Liouville generalized…