E. T. Jaynes' subjectivism vs measurement of distributions












2












$begingroup$


In his paper, E. T. Jaynes argues that entropy is a measure of our ignorance about a system. As such, the probability distribution of states ${p_k}$ has to be chosen in the most unbiased way, thus maximizing the entropy constrained to all the available information. This is a subjectivist point of view because treats probabilities as description of our ignorance, rather than as an intrinsic property of the system. He also claims that the reason statistical mechanics works is that the distributions are sharply peaked and, as long as the peak is at the correct position, its shape is not that relevant.



With the development of computers and experiments, however, now we are able to simulate distributions of states in a system or measure actual equilibrium fluctuations at a high resolution (with optical tweezers, for example). Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states. Measurements show that these are indeed the distributions that maximize entropy (at constant temperature, for instance, it's the Boltzmann distribution). How would a subjectivist argue then that the probability of states are due to our lack of information about the system? If I can measure those distributions, they look very objective to me.






statistical-mechanics entropy probability information







share|cite|improve this question









$endgroup$

















    2












    $begingroup$


    In his paper, E. T. Jaynes argues that entropy is a measure of our ignorance about a system. As such, the probability distribution of states ${p_k}$ has to be chosen in the most unbiased way, thus maximizing the entropy constrained to all the available information. This is a subjectivist point of view because treats probabilities as description of our ignorance, rather than as an intrinsic property of the system. He also claims that the reason statistical mechanics works is that the distributions are sharply peaked and, as long as the peak is at the correct position, its shape is not that relevant.



    With the development of computers and experiments, however, now we are able to simulate distributions of states in a system or measure actual equilibrium fluctuations at a high resolution (with optical tweezers, for example). Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states. Measurements show that these are indeed the distributions that maximize entropy (at constant temperature, for instance, it's the Boltzmann distribution). How would a subjectivist argue then that the probability of states are due to our lack of information about the system? If I can measure those distributions, they look very objective to me.






    statistical-mechanics entropy probability information







    share|cite|improve this question









    $endgroup$















      2












      2








      2





      $begingroup$


      In his paper, E. T. Jaynes argues that entropy is a measure of our ignorance about a system. As such, the probability distribution of states ${p_k}$ has to be chosen in the most unbiased way, thus maximizing the entropy constrained to all the available information. This is a subjectivist point of view because treats probabilities as description of our ignorance, rather than as an intrinsic property of the system. He also claims that the reason statistical mechanics works is that the distributions are sharply peaked and, as long as the peak is at the correct position, its shape is not that relevant.



      With the development of computers and experiments, however, now we are able to simulate distributions of states in a system or measure actual equilibrium fluctuations at a high resolution (with optical tweezers, for example). Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states. Measurements show that these are indeed the distributions that maximize entropy (at constant temperature, for instance, it's the Boltzmann distribution). How would a subjectivist argue then that the probability of states are due to our lack of information about the system? If I can measure those distributions, they look very objective to me.






      statistical-mechanics entropy probability information







      share|cite|improve this question









      $endgroup$




      In his paper, E. T. Jaynes argues that entropy is a measure of our ignorance about a system. As such, the probability distribution of states ${p_k}$ has to be chosen in the most unbiased way, thus maximizing the entropy constrained to all the available information. This is a subjectivist point of view because treats probabilities as description of our ignorance, rather than as an intrinsic property of the system. He also claims that the reason statistical mechanics works is that the distributions are sharply peaked and, as long as the peak is at the correct position, its shape is not that relevant.



      With the development of computers and experiments, however, now we are able to simulate distributions of states in a system or measure actual equilibrium fluctuations at a high resolution (with optical tweezers, for example). Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states. Measurements show that these are indeed the distributions that maximize entropy (at constant temperature, for instance, it's the Boltzmann distribution). How would a subjectivist argue then that the probability of states are due to our lack of information about the system? If I can measure those distributions, they look very objective to me.






      statistical-mechanics entropy probability information




      statistical-mechanics entropy probability information






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 5 hours ago









      BotondBotond

      1203




      1203






















          1 Answer
          1






          active

          oldest

          votes


















          4












          $begingroup$


          Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states.




          This is a misunderstanding. One never measures probability, the verb does not apply to the noun. In such simulations/calculations one may record some numbers, such as number of times the system was found in some region of phase space (or number of times system assumed some definite microstate). Such numbers can be divided by total number of observations or total number of time points, but this only gives frequency of occurences in that simulation, an artefact that depends on initial condition that may not repeat itself with different initial condition. It can serve as estimate of the probability, but itself is not the probability, which is supposed to abstract from details such as the initial condition. Jaynes provides a coherent way to think about the probability and a way to find probabilities in a number of cases of interest in statistical physics, using the maximum information entropy principle. Of course, one should test, if possible, usefulness of so determined probabilities, for example through computer simulations of concrete cases.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
            $endgroup$
            – Botond
            2 hours ago






          • 1




            $begingroup$
            The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
            $endgroup$
            – Ján Lalinský
            1 hour ago













          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "151"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: false,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: null,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f461038%2fe-t-jaynes-subjectivism-vs-measurement-of-distributions%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          4












          $begingroup$


          Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states.




          This is a misunderstanding. One never measures probability, the verb does not apply to the noun. In such simulations/calculations one may record some numbers, such as number of times the system was found in some region of phase space (or number of times system assumed some definite microstate). Such numbers can be divided by total number of observations or total number of time points, but this only gives frequency of occurences in that simulation, an artefact that depends on initial condition that may not repeat itself with different initial condition. It can serve as estimate of the probability, but itself is not the probability, which is supposed to abstract from details such as the initial condition. Jaynes provides a coherent way to think about the probability and a way to find probabilities in a number of cases of interest in statistical physics, using the maximum information entropy principle. Of course, one should test, if possible, usefulness of so determined probabilities, for example through computer simulations of concrete cases.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
            $endgroup$
            – Botond
            2 hours ago






          • 1




            $begingroup$
            The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
            $endgroup$
            – Ján Lalinský
            1 hour ago


















          4












          $begingroup$


          Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states.




          This is a misunderstanding. One never measures probability, the verb does not apply to the noun. In such simulations/calculations one may record some numbers, such as number of times the system was found in some region of phase space (or number of times system assumed some definite microstate). Such numbers can be divided by total number of observations or total number of time points, but this only gives frequency of occurences in that simulation, an artefact that depends on initial condition that may not repeat itself with different initial condition. It can serve as estimate of the probability, but itself is not the probability, which is supposed to abstract from details such as the initial condition. Jaynes provides a coherent way to think about the probability and a way to find probabilities in a number of cases of interest in statistical physics, using the maximum information entropy principle. Of course, one should test, if possible, usefulness of so determined probabilities, for example through computer simulations of concrete cases.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
            $endgroup$
            – Botond
            2 hours ago






          • 1




            $begingroup$
            The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
            $endgroup$
            – Ján Lalinský
            1 hour ago
















          4












          4








          4





          $begingroup$


          Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states.




          This is a misunderstanding. One never measures probability, the verb does not apply to the noun. In such simulations/calculations one may record some numbers, such as number of times the system was found in some region of phase space (or number of times system assumed some definite microstate). Such numbers can be divided by total number of observations or total number of time points, but this only gives frequency of occurences in that simulation, an artefact that depends on initial condition that may not repeat itself with different initial condition. It can serve as estimate of the probability, but itself is not the probability, which is supposed to abstract from details such as the initial condition. Jaynes provides a coherent way to think about the probability and a way to find probabilities in a number of cases of interest in statistical physics, using the maximum information entropy principle. Of course, one should test, if possible, usefulness of so determined probabilities, for example through computer simulations of concrete cases.






          share|cite|improve this answer









          $endgroup$




          Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states.




          This is a misunderstanding. One never measures probability, the verb does not apply to the noun. In such simulations/calculations one may record some numbers, such as number of times the system was found in some region of phase space (or number of times system assumed some definite microstate). Such numbers can be divided by total number of observations or total number of time points, but this only gives frequency of occurences in that simulation, an artefact that depends on initial condition that may not repeat itself with different initial condition. It can serve as estimate of the probability, but itself is not the probability, which is supposed to abstract from details such as the initial condition. Jaynes provides a coherent way to think about the probability and a way to find probabilities in a number of cases of interest in statistical physics, using the maximum information entropy principle. Of course, one should test, if possible, usefulness of so determined probabilities, for example through computer simulations of concrete cases.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 3 hours ago









          Ján LalinskýJán Lalinský

          15.1k1334




          15.1k1334












          • $begingroup$
            I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
            $endgroup$
            – Botond
            2 hours ago






          • 1




            $begingroup$
            The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
            $endgroup$
            – Ján Lalinský
            1 hour ago




















          • $begingroup$
            I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
            $endgroup$
            – Botond
            2 hours ago






          • 1




            $begingroup$
            The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
            $endgroup$
            – Ján Lalinský
            1 hour ago


















          $begingroup$
          I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
          $endgroup$
          – Botond
          2 hours ago




          $begingroup$
          I agree that all you can measure is frequency of occurences. At equilibrium, however, these frequencies converge to well defined values as you increase the number of measurements, independently of the initial conditions. I'm biased because I was trained in the objectivist spirit, but I'm still having hard time to see why it's obvious to measure frequencies that are precisely the same as the "working probabilities" "guessed" via the maximum entropy principle.
          $endgroup$
          – Botond
          2 hours ago




          1




          1




          $begingroup$
          The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
          $endgroup$
          – Ján Lalinský
          1 hour ago






          $begingroup$
          The match between observed frequencies and maxent probabilities isn't obvious, and it isn't always the case. However, it just is the most probable thing to happen, if all available knowledge was taken into consideration when predicting the probabilities. It is like with the law of large numbers: there is no guarantee that statistics on large number of experiments will show agreement with the probability derivation, but if the derivation is right, it is very probable.
          $endgroup$
          – Ján Lalinský
          1 hour ago




















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Physics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid …



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f461038%2fe-t-jaynes-subjectivism-vs-measurement-of-distributions%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          -

          Popular posts from this blog

          Loup dans la culture

          Image
          Loups sur une enluminure du Bestiaire d'Aberdeen Le loup est l'animal le plus emblématique de l'histoire de l'Eurasie, il était à l'honneur durant l'Antiquité chez la totalité des anciens peuples européens [ 1 ] . Sommaire 1 Le loup dans la mythologie 2 Les loups dans le folklore 2.1 L'évolution des mentalités 2.2 Le loup dans la psychanalyse 3 Le loup dans les œuvres culturelles 3.1 Le loup dans la littérature 3.1.1 Fables 3.1.2 Poésie 3.1.3 Romans 3.1.4 Littérature jeunesse 3.1.4.1 Quelques titres d'albums contemporains 3.1.5 Bande dessinée 3.2 Le loup à l'écran 3.2.1 Le cinéma et la télévision 3.2.2 Documentaires 3.2.3 Dessins animés 3.2.4 Jeux vidéo 3.3 Le loup en peinture et en sculpture 3.4 Le loup dans les œuvres musicales 4 Le loup et les noms propres 5 Bibliographie 6 Notes et références 7 Voir aussi 7.1 Articles connexes ...
          Read more

          How to solve the problem of ntp “Unable to contact time server” from KDE?

          Image
          1 0 I want to set date and time automatically but this error appears when I try to .. I'm using openSUSE, I tried different servers but it didn't work either, help please! It doesn't seem to be a network problem: $ ping pool.ntp.org 64 bytes from 41.78.128.17: icmp_seq=1 ttl=41 time=260 ms To the question of whether ntpd is installed and running: $ ps -C ntpd PID TTY TIME CMD i.e. there's no ntpd process running. $ rpm -qa | grep ntp yast2-ntp-client-3.1.12-1.7.noarch ntp-4.2.6p5-25.2.1.i586 Further information from the comments: $ sudo ntpdate pool.ntp.org 25 Sep 19:41:51 ntpdate[3162]: no server suitable for synchronization found networking kde opensuse ntp ntpd sh...
          Read more

          ASUS Zenbook UX433/UX333 — Configure Touchpad-embedded numpad on Linux

          Image
          0 1 I have an ASUS Zenbook UX433,on which ASUS decided to innovate by embedding a Numpad inside the touchpad (see picture 1). Toggling between classic touchpad mode and numpad (also turns the touchpad LEDs on) can be done through the golden button in the top-right corner of the touchpad. However, on my Manjaro arch Linux config, this behavior does not work by default and I can only use the touchpad, no numpad. Has anyone been able to configure the numpad to work on Linux, or have any idea how this could be achieved? EDIT1: I have had a look at the official Windows drivers for the UX433FA TouchPad, but was not able to make anything of it. I tried installing them on Linux using tools like NDISWrapper, but they do not detect the TouchPad/Numpad hardware, and my understanding of drivers is too limited. ...
          Read more